smoothplanegalrep

Function: smoothplanegalrep
Section: modular_forms
C-Name: SmoothGalRep
Prototype: GGGLGDGD0,U,
Help: smoothplanegalrep(f,l,p,e,P,{Chi},{a}): Computes p-adically the Galois representation afforded by the l-torsion of the smooth plane curve C:f(x,y)=0. p must be a prime of good reduction of this model. P must be a pair of distinct vectors of distinct n points on C, where n = d-1 if d is odd and n = d/2-1 if d is even, and where d is the total degree of f. e is a guess for the required p-adic accuracy. If present, Chi must divide mod l the local L factor of C at p, and be coprime with is cofactor; in this case, we compute the Galois representation attached to the subspace of the l-torsion where Frob_p acts with characteristic polynomial Chi. If a is present, work in the unramified extension of Qp of degree a; else a is chosen automatically.
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