curve #3936

y² + xy + y = x³ − 309560339035671289x + 66292753193209087922645466

a-invariants: [1, 0, 1, -309560339035671289, 66292753193209087922645466]
c-invariants: [14858896273712221849, -57276938781220996375734015613]
rank (lower bound): ≥ 6
torsion subgroup: ℤ/6ℤ
conductor (N): 79182482567274710
discriminant (Δ): 243614968810567548719341565486758776559493830010
Faltings height: 8.5426
naive height: 132.4354
primes of bad reduction: 2, 5, 13, 17, 23, 31, 37, 103, 113, 116689
regulator: 16669686.620474272961722705145753147726607757175043
submitted by: Odbayar Shinebayar
submitted at: 2026-10-05 04:29:44 UTC
last updated: 2026-10-05 04:29:44 UTC

Witness: 6 independent points log in to add more points →

(1286296011/4, -85886949269/8)
(70070563791774/218089, -12538261265553497/101847563)
(41546478786384/17161, 261265762890687873363/2248091)
(17643543024/49, -421933119992854/343)
(3994655839307679/12432676, -57249385387188813033/43837615576)
(6311560795625194746/19635015625, -18102386253489785723830831/2751356564453125)

Commentary

Unlisted rational-isogeny neighbor of curve#3712 (source contributor: Michael Rubinstein). Source equation and witness provenance are credited to that entry. Exact rank 6: 6 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 04:29:45 UTC · history