curve #3955

y² = x³ + x² − 2555814488519354050x + 1539527968384732970714035448

a-invariants: [0, 1, 0, -2555814488519354050, 1539527968384732970714035448]
c-invariants: [122679095448928994416, -1330152165420483859390500593536]
rank (lower bound): ≥ 8
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
conductor (N): 6913619279132804573280
discriminant (Δ): 44580606737138363511524505735362643317555585630049000000
Faltings height: 9.4626
naive height: 138.7683
primes of bad reduction: 2, 3, 5, 11, 29, 41, 59, 67, 97, 137, 419, 50033
regulator: 608753261.157211326494473693247462725790603814977961624
submitted by: Odbayar Shinebayar
submitted at: 2026-10-05 04:33:45 UTC
last updated: 2026-10-05 04:33:45 UTC

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

(-3447468967771/3844, -13291647002705364975/238328)
(-1685096614, -32579214431940)
(8733770057546/8281, -3119040821660454900/753571)
(6629833910309/33124, 194040763471390600575/6028568)
(35503141176826/53361, 142461734718091050100/12326391)
(3983274729872474/3751969, -34651349232624230241780/7267563953)
(-1442256325831/784, -86886571908004875/21952)
(9228424270589666/11566801, 113078898344968242310800/39338690201)

Commentary

Unlisted rational-isogeny neighbor of curve#3668 (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 04:33:45 UTC · history