curve #3994

y² + xy + y = x³ − 254885870810757051x + 155139987952707713441282998

a-invariants: [1, 0, 1, -254885870810757051, 155139987952707713441282998]
c-invariants: [12234521798916338425, -134040949609491247111643018125]
rank (lower bound): ≥ 12
torsion subgroup: ℤ/2ℤ
conductor (N): 145059433532653065217081920420450
discriminant (Δ): -9337771897686435317629091295333931508053694494059750000
Faltings height: 9.2321
naive height: 134.1359
primes of bad reduction: 2, 3, 5, 11, 19, 41, 53, 61, 103, 109, 263, 353, 443, 619, 3931, 31069
regulator: 8801521254112256.0355955079841086995640143897429828106112984496
submitted by: Odbayar Shinebayar
submitted at: 2026-10-05 04:41:38 UTC
last updated: 2026-10-05 04:41:38 UTC

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

(-2833944860783/4096, 140682543539544359/262144)
(-11668950907991/40000, 114451437732138228127/8000000)
(1264039903243/2209, 1455924235353984328/103823)
(1007376152, 30341976774861)
(105456773552, 34245704359029186)
(629124230762063/546121, 15047998697400783044268/403583419)
(-5984376377743/10816, 12666286219016170779/1124864)
(11935674245707/74529, 221417400052477941304/20346417)
(798726167588321711/113827561, 712139797358894794278280404/1214426248309)
(129510118251671768/232593001, 48357753878032680317444367/3547275858251)
(-46304796115758292852952/89755861237849, 10391430431677528251912071617460473/850343169865348198493)
(1706080145352527730407/742476912241, 69206776773528806397860736483996/639770823447614711)

Commentary

Unlisted rational-isogeny neighbor of curve#3629 (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 04:41:38 UTC · history