curve #3962

y² + xy + y = x³ + x² − 1843541751890712259469525x + 960432014826931257852095990433322010

a-invariants: [1, 1, 1, -1843541751890712259469525, 960432014826931257852095990433322010]
c-invariants: [88490004090754188454537201, -829813260811132281814891592147799245801]
rank (lower bound): ≥ 9
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
conductor (N): 6830331854767804004039231385
discriminant (Δ): 2505342782817127150084980658321288763905817358738160710174995931908765625
Faltings height: 12.7531
naive height: 179.2348
primes of bad reduction: 3, 5, 11, 13, 17, 31, 41, 43, 73, 103, 127, 443, 821, 941, 10487
regulator: 101912616849.21663047909536922845312150662142299639349576
submitted by: Odbayar Shinebayar
submitted at: 2026-10-05 04:35:07 UTC
last updated: 2026-10-05 04:35:07 UTC

Witness: 9 independent points log in to add more points →

(717587027433, -83894796137064317)
(20181656783750103/2116, -2839452259710522641758187/97336)
(3511892478933, -6148143500458258067)
(95541170887963/36, -829850213347091245597/216)
(149310645003559483/181476, -1883050688602579241005367/77308776)
(-20261165574471093/33124, -8220156565202685941518381/6028568)
(-35549389952523/49, -474785953760879729681/343)
(330764022597537/169, 4838092243340016794251/2197)
(171495280535824155553/207965241, 92606529057432838939789250863/2999066740461)

Commentary

Unlisted rational-isogeny neighbor of curve#3680 (source contributor: Michael Rubinstein). Source equation and witness provenance are credited to that entry. Exact rank 9: 9 independent points certified by the unchanged ICARM verifier, with a matching unconditional upper bound computed using PARI/GP 2.17.2 ellrank. This is an additional representative of a known isogeny class, not a claim of a new world rank record.

last edited by Odbayar Shinebayar at 2026-10-05 04:35:07 UTC · history