curve #3946

y² + xy + y = x³ + x² − 3661223359692025x + 85264883940878971962542

a-invariants: [1, 1, 1, -3661223359692025, 85264883940878971962542]
c-invariants: [175738721265217201, -73668861042959841264765449]
rank (lower bound): ≥ 7
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
conductor (N): 526770622069324545
discriminant (Δ): 249322501944915053582849740376622474123140625
Faltings height: 7.5945
naive height: 119.1233
primes of bad reduction: 3, 5, 11, 31, 109, 421, 653, 1709, 2011
regulator: 12345919715.61070903784274750639396105535045886905622
submitted by: Odbayar Shinebayar
submitted at: 2026-10-05 04:31:52 UTC
last updated: 2026-10-05 04:31:52 UTC

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

(4476594942027993/107474689, -79044829707297277736347/1114190100863)
(32424882163/324, -4952916958420583/5832)
(21695346772221/32041, 100660857936214218311/5735339)
(60468702682935494401/195904497321, 461772382735805559754167777889/86709485463745131)
(600370659525949531153/15602792301369, 2269591283437659482379961235543/61631606893722700653)
(14225466041073201073/404339559129, -454151420009908016719302377/257110225840271133)
(299349638877653189175647433/7165834818257843809, 1385545734390723598099094731629829495463/19182278380425018222935897873)

Commentary

Unlisted rational-isogeny neighbor of curve#3661 (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 04:31:52 UTC · history