-1
0
152
1031:[504, 2]
2053:[1008, 2]
4099:[4196]
8209:[8291]
16411:[8280, 2]
32771:[32545]
65537:[65115]
131101:[130579]
262147:[261873]
524309:[525362]
1048583:[1048721]
2097169:[2099343]
4194319:[4190448]
8388617:[4196176, 2]
16777259:[16776451]
33554467:[33556544]
67108879:[33553348, 2]
134217757:[134207016]
268435459:[268450764]
536870923:[536886729]
1073741827:[1073696739]
2147483659:[2147445985]
4294967311:[4294892145]
8589934609:[8589800815]
17179869209:[17179907771]
34359738421:[34359891299]
68719476767:[68719109932]
137438953481:[137439150447]
274877906951:[274876963417]
549755813911:[549755723143]
1099511627791:[1099510624080]
2199023255579:[1099512197774, 2]
4398046511119:[4398049864270]
8796093022237:[8796090641581]
17592186044423:[17592179180564]
35184372088891:[35184377696395]
70368744177679:[70368735914810]
140737488355333:[140737466844674]
281474976710677:[281474967245574]
562949953421381:[562949910045019]
1125899906842679:[562949923357406, 2]
2251799813685269:[2251799812875502]
4503599627370517:[4503599672855988]
9007199254740997:[9007199395723803]
18014398509482143:[18014398460825440]
36028797018963971:[18014398463069820, 2]
72057594037928017:[36028797145369816, 2]
144115188075855881:[144115187446866113]
288230376151711813:[288230375567209858]
576460752303423619:[576460752721346915]
1152921504606847009:[1152921506693313952]
2305843009213693967:[2305843010596733829]
4611686018427388039:[4611686021547019756]
9223372036854775837:[9223372041689460430]
15
1
1
163663
121661
1
1023
494
0
1728
j
0
Mod(0, 5)
Mod(3, 5)
Mod(1, 2)*j
0
Mod(1, 3)*j
[0, D*a2, 0, D^2*a4, D^3*a6]
[a1, T*a1^2 + a2, a3, a4, T*a3^2 + a6]
[a1, a2, a3, a4, a6]
[0, -a1^2 - 4*a2, 0, 8*a3*a1 + 16*a4, -16*a3^2 - 64*a6]
[-a1, a1^2 + 5*a2, -5*a3, 10*a3*a1 + 25*a4, 25*a3^2 + 125*a6]
-8
-4
133304232
133304232
a
a
[5, -66, 148, 665, -15802]
[3, -15, -40, 40, -181]
[3, -15, -40, 40, -181]
[5, -70, -300, 1956, -28305]
8*x^9 + 54*x^8 + 393*x^7 + 2373*x^6 + 6993*x^5 + 15267*x^4 + 19998*x^3 + 473
4*x^2 - 25880*x - 30932
[0, 0]
[x, 1]
[x^4 - 13*x^2 - 74*x - 41, 4*x^3 + 9*x^2 + 26*x + 37]
[x^16 - 260*x^14 - 5968*x^13 - 39963*x^12 - 140444*x^11 - 195486*x^10 + 5215
64*x^9 + 5378114*x^8 + 23699984*x^7 + 74549288*x^6 + 183951360*x^5 + 3366091
54*x^4 + 444753656*x^3 + 432135644*x^2 + 255731272*x + 49749605, 16*x^15 + 1
80*x^14 + 1792*x^13 + 14753*x^12 + 84148*x^11 + 414370*x^10 + 1658348*x^9 + 
4652985*x^8 + 9212312*x^7 + 10904612*x^6 + 434120*x^5 - 24648228*x^4 - 39304
176*x^3 - 13741184*x^2 + 25100064*x + 25859152]
[x^25 - 650*x^23 - 23335*x^22 - 259290*x^21 - 1456154*x^20 - 2820445*x^19 + 
20761370*x^18 + 277111495*x^17 + 2007242185*x^16 + 11282671667*x^15 + 529194
54495*x^14 + 207385350880*x^13 + 677127946605*x^12 + 1857857835015*x^11 + 43
12300313262*x^10 + 8526087679330*x^9 + 14394585463670*x^8 + 20512909438825*x
^7 + 23836827014955*x^6 + 20324637565929*x^5 + 7866409553255*x^4 - 796635515
1205*x^3 - 15373355872840*x^2 - 10304273387855*x - 2425203075812, 25*x^24 + 
450*x^23 + 6865*x^22 + 90410*x^21 + 848806*x^20 + 6747580*x^19 + 45352495*x^
18 + 229321140*x^17 + 838958290*x^16 + 2007441886*x^15 + 1506282910*x^14 - 1
1941908510*x^13 - 67097680775*x^12 - 197749423840*x^11 - 360107712461*x^10 -
 248110872190*x^9 + 863441551840*x^8 + 3852505140470*x^7 + 8796991424540*x^6
 + 14201708642530*x^5 + 17446507273700*x^4 + 16338035413000*x^3 + 1142822256
7925*x^2 + 5633997157650*x + 1472351694025]
[0]
[-23338430276487649199700397847721116081702650343430925719105465344187224269
2167848859501069746367317057135733659821516586965453870026354744714986684965
8323996212283434950398700511439/21452304628477972409549628569820513272484339
3023834534814913254065684077308619895779034479691808535960623339165042624323
5345631919723231687684699452030828176986716708998958804636224, -892721634620
8423324340896231392069270729522715981007828685033969863523382353428674866926
4734542739355918998020644016664732197288414787069129806148688960193235312780
7158822883693587635120259554260938849967680317634128924102700969620674883736
9307779952513049787052947107461/31420343828112469950094830391399473730286380
5713026983524763427660191121031569408909200906270720147570836507805210795709
8988916304745235223129078126602318052803199405011168522054272192266092941904
104143227672460543588095008724194999641591292020853488313837016518733957632]
[-1, 1]
[-1, -3]
[833245230963211172586751702962398963656841653/30025043966406435914574252820
2802293592821136, -572865877831905829779071583256995923720966703129995025914
40045201397/5202660393781989115440421988056492168066969880055771334597510887
616]
[-10325327/6270016, -17317169781/15700120064]
[-10325327/6270016, -17317169781/15700120064]
16*x^33 + 20048*x^30 - 524864*x^27 - 20273280*x^24 - 35051520*x^21 - 1832755
20*x^18 - 818626560*x^15 - 1017937920*x^12 - 390856704*x^9 + 74973184*x^6 + 
102760448*x^3 + 4194304
[3.1096482423243803285501491221965830079, 1.55482412116219016427507456109829
15039 + 1.0643747452102737569438859937299427442*I]
[6.2192964846487606571002982443931660158, 3.10964824232438032855014912219658
30079 + 2.1287494904205475138877719874598854884*I]
[5.5614800275334595421263952543627169988, 2.78074001376672977106319762718135
84994 - 2.1374995527123861323185270948750077575*I]
[6.2192964846487606571002982443931660158, 3.10964824232438032855014912219658
30079 + 2.1287494904205475138877719874598854884*I]
[-1.1547274830668428355945002349018042438, -0.828886258466578582202749882549
09787812 + 0.52313677422798965199542236165917364573*I, -0.828886258466578582
20274988254909787812 - 0.52313677422798965199542236165917364573*I]
[10351, [1/2, -1, -2, 5/4], 1, [11, 1; 941, 1], [[1, 5, 0, 1], [1, 5, 0, 1]]
]
[10351, [1, -1, 0, -1], 1, [11, 1; 941, 1], [[1, 5, 0, 1], [1, 5, 0, 1]]]
  ***   at top-level: E.omega
  ***                   ^-----
  *** _.omega: incorrect type in omega [not defined over C] (t_VEC).
[9, [9], [[Mod(3, 7), Mod(5, 7)]]]
[0, 0, 0, 413748, 716503104, 0, 827496, 2866012416, -171187407504, -19859904
, -619058681856, -226311754192704000000, 97158364170048/2807086984375, Vecsm
all([1]), [Vecsmall([128, -1])], [0, 0, 0, 0, 0, 0, 0, [[2, 3]~]]]
[1/30, -13/150, -1/10, -79/500]
1
[36, [36], [[a^4 + a^3 + a^2, a^2]]]
1
[3, [3], [[0, 2]]]
1
[4, [4], [[Mod(3, 5), Mod(3, 5)]]]
[1 + 2*3 + 3^2 + 2*3^3 + 3^4 + 3^5 + 2*3^6 + 3^7 + O(3^8), 1 + 3 + 3^3 + 3^4
 + 2*3^5 + 2*3^6 + 2*3^7 + O(3^8), 3 + 2*3^3 + O(3^6), [1 + 2*3 + 3^2 + 2*3^
3 + 3^4 + 3^6 + 2*3^7 + O(3^8), 1 + 3 + 2*3^2 + 3^3 + 2*3^4 + 2*3^5 + 3^6 + 
3^7 + O(3^8)]]
[3^-1 + 2 + 2*3^2 + 2*3^5 + 2*3^6 + O(3^8)]~
[3^2 + 2*3^3 + 3^4 + 2*3^5 + 3^6 + 3^7 + 2*3^8 + 3^9 + O(3^10), 3 + 3^2 + 3^
4 + 3^5 + 2*3^6 + 2*3^7 + 2*3^8 + O(3^9), 3 + 2*3^3 + O(3^6), [3^-2 + 2*3^-1
 + 1 + 2*3 + 3^2 + 3^4 + 2*3^5 + O(3^6), 3^-2 + 3^-1 + 2 + 3 + 2*3^2 + 2*3^3
 + 3^4 + 3^5 + O(3^6)]]
error("incorrect type in obj_check (t_VEC).")
[2 + 2^6 + 2^10 + O(2^11), Mod(x, x^2 + (2 + 2^2 + 2^3 + 2^4 + 2^5 + 2^7 + 2
^8 + 2^9 + O(2^11))), 2^3 + 2^4 + O(2^8), [2^-3 + 2^2 + 2^4 + 2^7 + 2^10 + O
(2^11), 2^-3 + 2^2 + 2^5 + 2^6 + 2^10 + O(2^13)]]
x^-2 + 31/15*x^2 + 2501/756*x^4 + 961/675*x^6 + 77531/41580*x^8 + O(x^9)
[5.0000000000000000000000000000000000000, 4.99999999999999999999999999999999
99998]
[0]
[-1, -2*w]
[-1, 1/2*I]
[[-1, 1/2*I], [0.59200051084078635056480901325155142952, -6.5791855625999796
522076912731847814832*I]]
[1, 1]
x^-2 - 1/5*x^2 - 1/7*x^4 + 1/75*x^6 + 3/385*x^8 + 277/238875*x^10 - 2/5775*x
^12 + O(x^14)
x^-2 - 1/5*x^2 - 1/7*x^4 + 1/75*x^6 + O(x^7)
8.9760336058655702799613054290253052728
-8.9795585687185301843619815765809019104
0.0070737179180847219897019688523688143761 - 4.54459013280902760664280136539
71181201*I
[1, 2]
x^-2 + 103.98999607107861876118376809420672237*x^2 - 649.9550420035218272005
1926719405777425*x^4 + 3604.6397609543155221247400145868915015*x^6 - 18433.3
15162997447301537872827568145124*x^8 + 90164.1927526450698484311468148077532
96*x^10 - 425973.41586156854974946172781042993149*x^12 + O(x^14)
x^-2 + 103.98999607107861876118376809420672237*x^2 - 649.9550420035218272005
1926719405777425*x^4 + 3604.6397609543155221247400145868915015*x^6 + O(x^7)
15.663727422159594482268754503777038256
-39.480069718736152480166362703315829534
11.908171148288278998948804099769395642 + 1.97957325252946376553721096563444
46755*I
[1, 3]
x^-2 + 103.98999607107861876118376809420672237*x^2 - 649.9550420035218272005
1926719405777425*x^4 + 3604.6397609543155221247400145868915015*x^6 - 18433.3
15162997447301537872827568145124*x^8 + 90164.1927526450698484311468148077532
96*x^10 - 425973.41586156854974946172781042993149*x^12 + O(x^14)
x^-2 + 103.98999607107861876118376809420672237*x^2 - 649.9550420035218272005
1926719405777425*x^4 + 3604.6397609543155221247400145868915015*x^6 + O(x^7)
15.663727422159594482268754503777038256
-39.480069718736152480166362703315829534
11.908171148288278998948804099769395642 + 1.97957325252946376553721096563444
46755*I
[2, 1]
x^-1 + 1/15*x^3 + 1/35*x^5 - 1/525*x^7 - 1/1155*x^9 - 277/2627625*x^11 + 2/7
5075*x^13 + O(x^15)
x^-1 + 1/15*x^3 + 1/35*x^5 - 1/525*x^7 + O(x^8)
3.0025857981852417376980007365038576528
-3.0023507303355942712341893343171384978*I
1.4945837634650773441141478432745008118 - 1.49552579635851441107083905597206
14467*I
[2, 2]
x^-1 - 34.663332023692872920394589364735574123*x^3 + 129.9910084007043654401
0385343881155485*x^5 - 514.94853727918793173210571636955592878*x^7 + 2048.14
61292219385890597636475075716805*x^9 - 8196.74479569500634985737698316434120
88*x^11 + 32767.185835505273057650902139263840884*x^13 + O(x^15)
x^-1 - 34.663332023692872920394589364735574123*x^3 + 129.9910084007043654401
0385343881155485*x^5 - 514.94853727918793173210571636955592878*x^7 + O(x^8)
2.0876703200272312306836757817491311900
0
1.8018229730105461594800210664505892466 - 4.22108966565276293974646245627813
69159*I
[2, 3]
x^-1 - 34.663332023692872920394589364735574123*x^3 + 129.9910084007043654401
0385343881155485*x^5 - 514.94853727918793173210571636955592878*x^7 + 2048.14
61292219385890597636475075716805*x^9 - 8196.74479569500634985737698316434120
88*x^11 + 32767.185835505273057650902139263840884*x^13 + O(x^15)
x^-1 - 34.663332023692872920394589364735574123*x^3 + 129.9910084007043654401
0385343881155485*x^5 - 514.94853727918793173210571636955592878*x^7 + O(x^8)
2.0876703200272312306836757817491311900
0
1.8018229730105461594800210664505892466 - 4.22108966565276293974646245627813
69159*I
[3, 1]
x + 1/60*x^5 + 1/210*x^7 - 1/10080*x^9 - 1/138600*x^11 - 167/259459200*x^13 
- 19/1513512000*x^15 + O(x^17)
x + 1/60*x^5 + 1/210*x^7 - 1/10080*x^9 + O(x^10)
0.33340409272605175654322174351877926789
0.33339973807064633526799756411632693200*I
0.33307632454406929865753194192439552171 + 0.3330414840427217068846417452694
8964209*I
[3, 2]
x - 8.6658330059232182300986473411838935307*x^5 + 21.66516806678406090668397
5573135259142*x^7 - 26.820236316624371444380506060914371291*x^9 + 17.0678844
10182821575498030395896430672*x^11 + 0.9724196316598484235781214649285975622
3*x^13 - 15.440886182405758633317637416815798050*x^15 + O(x^17)
x - 8.6658330059232182300986473411838935307*x^5 + 21.66516806678406090668397
5573135259142*x^7 - 26.820236316624371444380506060914371291*x^9 + O(x^10)
0.30631122697380979289268115078987850649
0.E-38
0.53021646242894349905972369056429285872 + 0.3781418838145237834855647058271
9409288*I
[3, 3]
x - 8.6658330059232182300986473411838935307*x^5 + 21.66516806678406090668397
5573135259142*x^7 - 26.820236316624371444380506060914371291*x^9 + 17.0678844
10182821575498030395896430672*x^11 + 0.9724196316598484235781214649285975622
3*x^13 - 15.440886182405758633317637416815798050*x^15 + O(x^17)
x - 8.6658330059232182300986473411838935307*x^5 + 21.66516806678406090668397
5573135259142*x^7 - 26.820236316624371444380506060914371291*x^9 + O(x^10)
0.30631122697380979289268115078987850649
0.E-38
0.53021646242894349905972369056429285872 + 0.3781418838145237834855647058271
9409288*I
[4, 1]
0
0
-1.0984000330177788282680372407424344829
-1.0984130942966868400436474225688716324 + 1.5707963267948966192313216916397
514421*I
-0.75286232322707031868584884787482252469 + 0.785345859584418994173505759767
90041015*I
[4, 2]
0
0
-1.1831536122930622250712755356827420688
-1.2506870224867757820652851907990498543
-0.42886850134944751864186009377385060418 + 0.619519575104929600932212172490
11490053*I
[4, 3]
0
0
-1.1831536122930622250712755356827420688
-1.2506870224867757820652851907990498543
-0.42886850134944751864186009377385060418 + 0.619519575104929600932212172490
11490053*I
[2.5135797437238231405782694715779164652, 1.25678987186191157028913473578895
82326 + 0.78959476569186174055147277865716603189*I]
[3.1415926535897932384626433832795028842, 9.42477796076937971538793014983850
86526*I]
(x)->elleisnum(x,2)
-2.9936282668967606065680548947245432597 - 7.1637767384648910133063235008836
078048*I
157.90045350239951165298459055643475560
157.90045350239951165298459055643475560
(x)->real(elleisnum(x,4,1))
-3.9999999999999999999999999999999999999
2079.7999214215723752236753618841344474
2079.7999214215723752236753618841344474
(x)->real(elleisnum(x,6,1))
-4.0000000000000000000000000000000000000
-18198.741176098611161614539481433617679
-18198.741176098611161614539481433617679
(x)->real(elleisnum(x,10))
-41471.999999999999999999999999999999998
98106527293.111533926136928277796284706
98106527293.111533926136928277796284706
-1
[0]
347813742467679407541/38941611811810745401
[0.49999999999999999999999999999999999982 + 0.999999999999999999999999999999
99999992*I, 1.5617041082089070087003342842479112066 + 0.56028539298876740518
391807553710802962*I]
3 + 11^2 + 2*11^3 + 3*11^4 + O(11^5)
Mod((2 + 3 + O(3^4))*x + (2*3 + 3^2 + O(3^4)), x^2 + (1 + 3 + 2*3^4 + 3^8 + 
2*3^9 + O(3^10)))
Mod((1 + 3 + 3^3 + 3^4 + 2*3^6 + 2*3^8 + 2*3^9 + O(3^10))*x + (1 + 3 + 3^2 +
 3^5 + 2*3^6 + 2*3^7 + 2*3^8 + 3^9 + O(3^10)), x^2 + (3 + 3^3 + 2*3^4 + 3^5 
+ 2*3^6 + 3^7 + 2*3^8 + 3^9 + 2*3^10 + 3^11 + 2*3^12 + O(3^13)))
Mod((2^3 + 2^7 + O(2^8))*x + (1 + 2 + 2^2 + 2^3 + 2^4 + O(2^6)), x^2 + (1 + 
2^2 + 2^4 + 2^5 + 2^7 + 2^8 + 2^9 + O(2^13)))
[Mod(0, 11), Mod(0, 11), Mod(0, 11), Mod(1, 11), Mod(1, 11), Mod(0, 11), Mod
(2, 11), Mod(4, 11), Mod(10, 11), Mod(7, 11), Mod(5, 11), Mod(10, 11), Mod(9
, 11), Vecsmall([3]), [11, [9, 5, [6, 0, 0, 0]]], [0, 0, 0, 0]]
1
[0.86602540378443864676372317075293618347 - 1/2*I, -0.8660254037844386467637
2317075293618348 - 1/2*I]
[-2, 3]
[0, 1]
[1, 0, 0, 0]
0.035247504442186170440172838583518049039
[0, 0, 0, 1, 1, 0, 2, 4, -1, -48, -864, -496, 6912/31, Vecsmall([1]), [Vecsm
all([128, -1])], [0, 0, 0, 0, 0, 0, 0, [[2, 3]~]]]
[0, 0, 0, 1/16, 1/64, 0, 1/8, 1/16, -1/256, -3, -27/2, -31/256, 6912/31, Vec
small([1]), [Vecsmall([128, -1])], [0, 0, 0, 0, 0, 0, 0, [[2, 3]~, [1/2, 0, 
0, 0], [0, 0, 0, 1, 1, 0, 2, 4, -1, -48, -864, -496, 6912/31, Vecsmall([1]),
 [Vecsmall([128, -1])], [0, 0, 0, 0, 0, 0, 0, [[2, 3]~]]]]]]

0
20 0 0 -16 0 -4 14 8 0 0 0 26 0 2 0 -28 
1728
0 0 -22 0 -14 0 -22 0 0 26 0 18 0 -14 2 0 
-3375
16 0 -10 0 -22 24 0 -20 0 0 4 0 8 -18 -26 0 
8000
0 -18 6 22 0 0 0 2 0 0 18 0 0 22 0 0 
54000
20 0 0 16 0 4 -14 -8 0 0 0 26 0 2 0 -28 
-32768
0 0 3 0 0 0 23 16 0 0 21 25 -15 0 0 -20 
287496
0 0 22 0 -14 0 22 0 0 -26 0 -18 0 14 2 0 
-884736
0 7 23 -9 11 0 18 -24 0 0 0 0 17 0 -22 -25 
-12288000
20 0 0 -23 0 19 14 25 0 0 0 7 0 23 0 -11 
16581375
16 0 10 0 22 24 0 -20 0 0 -4 0 8 -18 -26 0 
-884736000
11 0 0 -13 0 0 0 0 -25 -2 0 -6 0 -27 -10 0 
-147197952000
-21 -16 0 0 -23 1 5 7 20 -25 0 11 0 13 0 -27 
-262537412640768000
0 19 0 0 0 -21 0 0 4 -23 8 0 0 0 -25 -12 
4294985035
[0, 1, [5, 0, 0, 0], 1]
1
0
[6.2500000000000000000000000000000000000, -140.62500000000000000000000000000
000000]
error("incorrect type in checkell (t_VEC).")
[0, 0, 0, x^2, x, 0, 2*x^2, 4*x, -x^4, -48*x^2, -864*x, -64*x^6 - 432*x^2, -
6912*x^4/(-4*x^4 - 27), Vecsmall([0]), [Vecsmall([128, 0])], [0, 0, 0, 0]]
  ***   at top-level: ellminimalmodel(E)
  ***                 ^------------------
  *** ellminimalmodel: incorrect type in checkell over Q (t_VEC).
  ***   at top-level: ellweilpairing(E,[0]
  ***                 ^--------------------
  *** ellweilpairing: incorrect type in checkell over Fq (t_VEC).
  ***   at top-level: ellinit([1])
  ***                 ^------------
  *** ellinit: incorrect type in ellxxx [not an elliptic curve (ell5)] (t_VEC).
  ***   at top-level: ellinit([1,1],quadge
  ***                 ^--------------------
  *** ellinit: incorrect type in elliptic curve base_ring (t_QUAD).
  ***   at top-level: ellinit([Mod(1,2),1]
  ***                 ^--------------------
  *** ellinit: incorrect type in elliptic curve base_ring (t_VEC).
  ***   at top-level: ellinit([O(2),1],ffg
  ***                 ^--------------------
  *** ellinit: incorrect type in elliptic curve base_ring (t_VEC).
  ***   at top-level: ellinit([O(2),1],1.)
  ***                 ^--------------------
  *** ellinit: incorrect type in elliptic curve base_ring (t_VEC).
[0, 0, 0, 1, 2, 0, 2, 8, -1, -48, -1728, -1792, 432/7, Vecsmall([0]), [Vecsm
all([128, -1])], [0, 0, 0, 0]]
[0, 0, 0, 0, 1, 0, 0, 4, 0, 0, 1, 3, 0, Vecsmall([4]), [0, [Vecsmall([0]), V
ecsmall([0, 1]), [Vecsmall([0, 1]), Vecsmall([0]), Vecsmall([0]), Vecsmall([
0])]]], [0, 0, 0, 0]]
  ***   at top-level: ellinit([ffgen(5),1]
  ***                 ^--------------------
  *** ellinit: inconsistent moduli in ellinit: 3 != 5
[0, 0, 0, 1.0000000000000000000000000000000000000, 1, 0, 2.00000000000000000
00000000000000000000, 4, -1.0000000000000000000000000000000000000, -48.00000
0000000000000000000000000000000, -864, -496.00000000000000000000000000000000
000, 222.96774193548387096774193548387096774, Vecsmall([0]), [Vecsmall([128,
 -1])], [0, 0, 0, 0]]
  ***   at top-level: ellinit([1.,Mod(1,3)
  ***                 ^--------------------
  *** ellinit: incorrect type in elliptic curve base_ring (t_VEC).
1
-1
1
1
x^-2 + Mod(-1/5*x, x^2 + 5)*x^2 + Mod(-1/15, x^2 + 5)*x^6 + Mod(2/975*x, x^2
 + 5)*x^10 + O(x^14)
x^-1 + Mod(1/15*x, x^2 + 5)*x^3 + Mod(1/105, x^2 + 5)*x^7 + Mod(-2/10725*x, 
x^2 + 5)*x^11 + O(x^15)
x + Mod(1/60*x, x^2 + 5)*x^5 + Mod(1/2016, x^2 + 5)*x^9 + Mod(23/51891840*x,
 x^2 + 5)*x^13 + O(x^17)
Mod(1, 1009)*x^-2 + Mod(807, 1009)*x^2 + Mod(148, 1009)*x^6 + Mod(368, 1009)
*x^10 + O(x^14)
Mod(1, 1009)*x^-1 + Mod(740, 1009)*x^3 + Mod(123, 1009)*x^7 + Mod(150, 1009)
*x^11 + O(x^15)
Mod(1, 1009)*x + Mod(185, 1009)*x^5 + Mod(101, 1009)*x^9 + Mod(990, 1009)*x^
13 + O(x^17)
-52760
-52832
[[1, -1], 2]
[[509051665/47782462464, -2265512629515497/10444864034930688], 12]
ellformalw
t^3 - t^5 + t^6 - t^7 - 3*t^8 + 9*t^9 - 2*t^10 - 21*t^11 + 45*t^12 - 21*t^13
 - 140*t^14 + 339*t^15 - 91*t^16 - 1051*t^17 + 2394*t^18 + O(t^19)
x^3 - x^5 + x^6 - x^7 + O(x^8)
t^3 - t^5 + t^6 - t^7 + O(t^8)
ellformalpoint
[t^-2 + 1 - t + 2*t^2 + t^3 - 5*t^4 + 3*t^5 + 5*t^6 - 19*t^7 + 22*t^8 + 33*t
^9 - 129*t^10 + 111*t^11 + 228*t^12 - 855*t^13 + O(t^14), -t^-3 - t^-1 + 1 -
 2*t - t^2 + 5*t^3 - 3*t^4 - 5*t^5 + 19*t^6 - 22*t^7 - 33*t^8 + 129*t^9 - 11
1*t^10 - 228*t^11 + 855*t^12 + O(t^13)]
[x^-2 + 1 - x + 2*x^2 + O(x^3), -x^-3 - x^-1 + 1 - 2*x + O(x^2)]
[t^-2 + 1 - t + 2*t^2 + O(t^3), -t^-3 - t^-1 + 1 - 2*t + O(t^2)]
ellformaldifferential
[1 - t^2 + 2*t^3 - 3*t^4 - 6*t^5 + 23*t^6 - 12*t^7 - 53*t^8 + 160*t^9 - 131*
t^10 - 470*t^11 + 1471*t^12 - 882*t^13 - 4257*t^14 + 12628*t^15 + O(t^16), t
^-2 + t - 2*t^2 - 2*t^3 + 11*t^4 - 9*t^5 - 18*t^6 + 78*t^7 - 94*t^8 - 175*t^
9 + 725*t^10 - 676*t^11 - 1603*t^12 + 6293*t^13 + O(t^14)]
[1 - x^2 + 2*x^3 - 3*x^4 + O(x^5), x^-2 + x - 2*x^2 + O(x^3)]
[1 - t^2 + 2*t^3 - 3*t^4 + O(t^5), t^-2 + t - 2*t^2 + O(t^3)]
ellformallog
t - 1/3*t^3 + 1/2*t^4 - 3/5*t^5 - t^6 + 23/7*t^7 - 3/2*t^8 - 53/9*t^9 + 16*t
^10 - 131/11*t^11 - 235/6*t^12 + 1471/13*t^13 - 63*t^14 - 1419/5*t^15 + 3157
/4*t^16 + O(t^17)
x - 1/3*x^3 + 1/2*x^4 - 3/5*x^5 + O(x^6)
t - 1/3*t^3 + 1/2*t^4 - 3/5*t^5 + O(t^6)
ellformalexp
t + 1/3*t^3 - 1/2*t^4 + 14/15*t^5 - 1/6*t^6 - 76/315*t^7 - 7/10*t^8 + 7547/1
1340*t^9 + 977/3780*t^10 - 5116/22275*t^11 - 78977/113400*t^12 + 3069607/608
1075*t^13 + 1651/2970*t^14 - 526660427/2554051500*t^15 - 5754943993/68108040
00*t^16 + O(t^17)
x + 1/3*x^3 - 1/2*x^4 + 14/15*x^5 + O(x^6)
t + 1/3*t^3 - 1/2*t^4 + 14/15*t^5 + O(t^6)
  ***   at top-level: ellformalw(e,0)
  ***                 ^---------------
  *** ellformalw: domain error in ellformalw: precision <= 0
  ***   at top-level: ellformalw(e,-1)
  ***                 ^----------------
  *** ellformalw: domain error in ellformalw: precision <= 0
242.47010035195076100129810400142304776
0
Total time spent: 432
