John Cremona on Sun, 26 Mar 2017 19:10:06 +0200 |
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Re: Selmer |
On 26 March 2017 at 17:19, Bill Allombert <Bill.Allombert@math.u-bordeaux.fr> wrote: > 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 ? TwoDescent(E); In this case it returns a list of 15 equations of the form y^2=quartic, each with a rational map to E, which represent the nontrivial elements of the 2-Selmer group (which does have order 16). Magma also has ThreeDescent(E) and FourDescent(E). John > > (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). > > Cheers, > Bill. >