Bill Allombert on Sun, 26 Mar 2017 18:19:22 +0200

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Re: Selmer

On Sun, Mar 26, 2017 at 07:16:00PM +0430, Benyamin Gholami wrote:
> Sure Sir !
> here you are:
> note that i created a rank 1 surface with torsion Z/2Z*Z/4Z  and i'm
> searching on this family for curves with rank 6 ( or fine if greater) with
> codes that you gave me before. my problem is in most of cases it just give
> "1" as lower bound and the selmer bounds are not indeed accurate. i upload
> denis simon script and then use sieving. any helps would be appreciated
> .thanks to you and Prof.Cremona (mr bellabas helped me to write S(E,N) , so
> thank to him so)

How do you compute the Selmer group with Magma ?

(The curves you are considering have large coefficients even after the
minimal model is taken. You are bound to have computational difficulties
with them.
You might want to increase the setting
LIM1 = 5;           \\ Limit for the search of trivial points on quartics
LIM3 = 50;          \\ Limit for the search of points on ELS quartics
LIMTRIV = 3;        \\ Limit for the search of trivial points on the elliptic curve

so that ellrank has more chance to find points).