curve #4000

y² = x³ − 628059450282317577588x + 6821121895212957859501945446512

a-invariants: [0, 0, 0, -628059450282317577588, 6821121895212957859501945446512]
c-invariants: [30146853613551243724224, -5893449317463995590609680865786368]
rank (lower bound): ≥ 13
torsion subgroup: ℤ/2ℤ
conductor (N): 1005791021107376101017459673931692686720
discriminant (Δ): -4244384256564033257321755973554888164941804316174226407767040000
Faltings height: 10.9379
naive height: 155.5183
primes of bad reduction: 2, 3, 5, 11, 13, 23, 67, 71, 73, 137, 151, 401, 619, 1583, 2789, 4513, 22303
regulator: 2801463064902547.493486050669211162584173921112603274430087172078
submitted by: Odbayar Shinebayar
submitted at: 2026-10-05 04:43:09 UTC
last updated: 2026-10-05 04:43:09 UTC

Witness: 13 independent points log in to add more points →

(58099898461, 12901660526457225)
(21428510917, 1789499901241773)
(34961603197, 5253304018016007)
(55973975713/4, -7031594975637969/8)
(28518565277, -3479103459064087)
(146685924313/4, -46029533907481731/8)
(233908363909/169, 5361082053573510675/2197)
(281141922017/16, -70413698128299217/64)
(3100928381/25, -324596410672570279/125)
(-4505092352771/289, 17593476207303072825/4913)
(4846202565293/289, -4924278097073207489/4913)
(5689293707301721/118336, -381336546672375168700125/40707584)
(6610080458199073/3844, -537358698102681303630831/238328)

Commentary

Unlisted rational-isogeny neighbor of curve#3009 (source contributor: Steps Unbounded). Source equation and witness provenance are credited to that entry. Exact rank 13: 13 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 04:43:09 UTC · history