curve #3958

y² + xy + y = x³ − x² − 76248070875164835915053630x − 164906452404742584689883133078189716628

a-invariants: [1, -1, 1, -76248070875164835915053630, -164906452404742584689883133078189716628]
c-invariants: [3659907402007912123922574225, 142479174877714062755368062584113566750375]
rank (lower bound): ≥ 9
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
conductor (N): 242574104114218087554953925
discriminant (Δ): 16622603937108405453705169063137391301409930370198192474891381756860442953515625
Faltings height: 13.9032
naive height: 190.4017
primes of bad reduction: 3, 5, 7, 31, 43, 47, 59, 73, 101, 137, 311, 353, 401, 937
regulator: 12029497804.730893430799764683536493466901274386733957294
submitted by: Odbayar Shinebayar
submitted at: 2026-10-05 04:34:25 UTC
last updated: 2026-10-05 04:34:25 UTC

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

(-1371789776237209833/253009, 1201379887950118035061338080/127263527)
(-14780098109253/4, -65180648679707193895/8)
(2140821808830591/169, -65981481909338839230440/2197)
(12200685791450991/1225, 342071149460384185854956/42875)
(133039993758342331/9025, 37513990523187045383111586/857375)
(-816523303500713/289, -25981762271459539500540/4913)
(11490965587565239/676, -1032456107866041158693145/17576)
(14531779649122154439/1437601, -16994752624900014572853862480/1723683599)
(-442203199213836555489/71944324, -5161497794186231213340001924985/610231756168)

Commentary

Unlisted rational-isogeny neighbor of curve#3694 (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 04:34:25 UTC · history