Z/2xZ/2 X400a family y^2=x(x+A)(x+B), with
A=q(121q-99p)(26p-23q)(75p-44q),
B=p(21q-74p)(25p-36q)(p+77q),
at T=p/q=19/61.
Family equations as posted by wgxli with curve #4252:
https://elliptic-rank.icarm.cloud/curve/4252
Section formulas from the Layr-Labs elliptic-rank-challenge-public repository, submission/research/x400a-family.gp, commit 7482bf9:
https://github.com/Layr-Labs/elliptic-rank-challenge-public/blob/7482bf9/submission/research/x400a-family.gp
This specialization was identified in a small-height rational-parameter enumeration with a Mestre–Nagao prescreen. A separate replay using the family sections returned rank bounds [8,8]. The eight displayed points were checked exactly on the global minimal model, and the torsion subgroup was computed as Z/2xZ/2.
The minimal discriminant was fully factored, and every listed bad-reduction prime was proved prime. The conductor is 42313351568007232235600.
The Wren ·