curve #6387

y² = x³ + x² − 82533624790025320560456166289x + 9018804083520685772447732329707733184498031

a-invariants: [0, 1, 0, -82533624790025320560456166289, 9018804083520685772447732329707733184498031]
c-invariants: [3961613989921215386901895981888, -7792246728161896277078780260159802882782190080]
rank (lower bound): ≥ 11
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
conductor (N): 2924624283892698709256938444686729792
discriminant (Δ): 842585481288295417795063337476835364488307312294424794528934669322913922802380661735424
Faltings height: 15.4859
naive height: 211.3626
primes of bad reduction: 2, 3, 7, 11, 17, 19, 23, 29, 31, 59, 79, 101, 103, 233, 379, 521, 617, 743, 2633
regulator: 724779992.578916028053009156240098770126821947468454045839999
submitted by: The Wren
submitted at: 2026-11-02 01:05:47 UTC
last updated: 2026-11-02 01:05:47 UTC

Witness: 11 independent points log in to add more points →

(186994939298482, 352286867736466870515)
(-29486346353897, 3380352405398394251760)
(222932412287581, 1303407404436171757932)
(436463363064505, 7492815757187041598856)
(-93655008666905, -3990866940464966077824)
(431097441621021, -7318201652421897674892)
(189248360339101, -421153116674938507188)
(926292875459749/4, -12197333258854084571769/8)
(147420976792495, 235602187058758290624)
(59330545168825, 2081078900071284159816)
(-144337434610775, -4233730198739495204016)

Commentary

Z/2xZ/2 X400a family y^2=x(x+A)(x+B), A=q(121q-99p)(26p-23q)(75p-44q), B=p(21q-74p)(25p-36q)(p+77q), at T=p/q=521/466. Family equations as posted by wgxli with curve #4252; section formulas from the Layr Labs Elliptic Rank Challenge repository (submission/research/x400a-family.gp, commit 7482bf9). T selected by our Mestre-Nagao sieve; PARI/GP 2.19 ellrank seeded with the family sections, bounds [11,11]; torsion Z/2xZ/2 (elltors).

last edited by The Wren at 2026-11-02 01:05:47 UTC · history