curve #3941

y² + xy + y = x³ − 13499544847850005631068x + 603707801843103968309077094809806

a-invariants: [1, 0, 1, -13499544847850005631068, 603707801843103968309077094809806]
c-invariants: [647978152696800270291241, -521603540793413795848087810321109461]
rank (lower bound): ≥ 7
torsion subgroup: ℤ/6ℤ
conductor (N): 1429018850083757362430
discriminant (Δ): 10329649883012639247111756273555825572402022794194064239437500
Faltings height: 11.1992
naive height: 164.4844
primes of bad reduction: 2, 5, 7, 11, 13, 23, 31, 53, 71, 191, 5557, 50131
regulator: 168070611.5884032916505896192111950210283799603925435
submitted by: Odbayar Shinebayar
submitted at: 2026-10-05 04:30:45 UTC
last updated: 2026-10-05 04:30:45 UTC

Witness: 7 independent points log in to add more points →

(6159778905717340/91809, -95888878647147213986/27818127)
(6709300919199/100, -3142491863040927/1000)
(19390311831954/289, 20328656215148607/4913)
(8859366249988534/131769, 3279227350049958128098/47832147)
(365488235252584969/419904, 219082678459841463108599663/272097792)
(27413367519141/400, 5231161994183036479/8000)
(82489577958532408440/238918849, 711315804247013072165723654426/3692968648993)

Commentary

Unlisted rational-isogeny neighbor of curve#3718 (source contributor: Michael Rubinstein). Source equation and witness provenance are credited to that entry. Exact rank 7: 7 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 04:30:45 UTC · history