curve #3952

y² + xy + y = x³ − x² − 105888428573108566622x + 283193309100327884365601962221

a-invariants: [1, -1, 1, -105888428573108566622, 283193309100327884365601962221]
c-invariants: [5082644571509211197841, -244679019039811391520088644968889]
rank (lower bound): ≥ 8
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
conductor (N): 2542465729285305792210
discriminant (Δ): 41338852347034765416937809751367732749436365216938297600000000
Faltings height: 10.5272
naive height: 149.9404
primes of bad reduction: 2, 3, 5, 11, 19, 31, 37, 43, 103, 389, 487, 140449
regulator: 35123287.8081877305329250082450023714422636440802987471
submitted by: Odbayar Shinebayar
submitted at: 2026-10-05 04:33:09 UTC
last updated: 2026-10-05 04:33:09 UTC

Witness: 8 independent points log in to add more points →

(-8082724039, 781676886062019)
(2029267361, -276901267357581)
(-5953978915, -838199284917333)
(-41645072181/4, -4056375718879523/8)
(27130187585, 4168861065617547)
(35065719585, 6299753306223467)
(-20747365271359/8281, 550036161383433374649/753571)
(487144345629/289, -1625717083104089753/4913)

Commentary

Unlisted rational-isogeny neighbor of curve#3667 (source contributor: Michael Rubinstein). Source equation and witness provenance are credited to that entry. Exact rank 8: 8 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 04:33:09 UTC · history