Function: ellglobalred
Section: elliptic_curves
C-Name: ellglobalred
Prototype: G
Help: ellglobalred(E): E being an elliptic curve, returns [N,[u,r,s,t],c,
 faN,L], where N is the conductor of E, [u,r,s,t] leads to the standard model
 for E, c is the product of the local Tamagawa numbers c_p, faN is factor(N)
 and L[i] is elllocalred(E, faN[i,1]),
 where the local coordinate change has been deleted and replaced by a 0.
Description:
 (gen):gen        ellglobalred($1)
Doc:
 calculates the arithmetic conductor, the global
 minimal model of $E$ and the global \idx{Tamagawa number} $c$.
 $E$ must be an \kbd{ell} structure as output by \kbd{ellinit}, defined over
 $\Q$. The result is a vector $[N,v,c,F,L]$, where

 \item $N$ is the arithmetic conductor of the curve,

 \item $v$ gives the coordinate change for $E$ over $\Q$ to the minimal
 integral model (see \tet{ellminimalmodel}),

 \item $c$ is the product of the local Tamagawa numbers $c_p$, a quantity
 which enters in the \idx{Birch and Swinnerton-Dyer conjecture},\sidx{minimal model}

 \item $F$ is the factorization of $N$ over $\Z$.

 \item $L$ is a vector, whose $i$-th entry contains the local data
 at the $i$-th prime divisor of $N$, i.e. \kbd{L[i] = elllocalred(E,F[i,1])},
 where the local coordinate change has been deleted and replaced by a 0.
