curve #3992

y² + xy + y = x³ − x² − 3362445101854435814267x + 75032628385235175926939685931755

a-invariants: [1, -1, 1, -3362445101854435814267, 75032628385235175926939685931755]
c-invariants: [161397364889012919084801, -64828190924116903858875330509154945]
rank (lower bound): ≥ 12
torsion subgroup: ℤ/2ℤ
conductor (N): 3744534523427843486091406117969518
discriminant (Δ): 904673183445661196541777760392525691645178617711431144600523392
Faltings height: 11.0750
naive height: 160.3145
primes of bad reduction: 2, 3, 11, 29, 31, 37, 163, 167, 199, 491, 1237, 2063, 3137, 4933, 5413
regulator: 720319151239051.78951140177746382471595320932957693277183370743
submitted by: Odbayar Shinebayar
submitted at: 2026-10-05 04:41:06 UTC
last updated: 2026-10-05 04:41:06 UTC

Witness: 12 independent points log in to add more points →

(69023561283, -13106915664976758)
(26538999992728163/591361, -1732759769219313830492334/454756609)
(48634385135, 5151408072971910)
(71632456803, 14203256845273674)
(504631173893, 356207396977413924)
(960853127431727/9409, -25759997968228080004794/912673)
(38351082900174595/314721, -6780366520307267860196366/176558481)
(73052849891957700943/1256773401, -388367820929274125358883923926/44553873838851)
(14051765332615/9, -52638203862679316542/27)
(350668205755/9, -48089100248422322/27)
(21632598858437/529, 29592331769530320474/12167)
(24265593349145621/648025, 665785225848204423507804/521660125)

Commentary

Unlisted rational-isogeny neighbor of curve#3632 (source contributor: Michael Rubinstein). Source equation and witness provenance are credited to that entry. Exact rank 12: 12 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 04:41:06 UTC · history