curve #4405

y² + xy = x³ − x² − 2599487089x + 39173361400609

a-invariants

[1, -1, 0, -2599487089, 39173361400609]

c-invariants

[124775380281, -33845222760914925]

rank (lower bound)

≥ 13

torsion subgroup

trivial

conductor (N)

230646920098311714063851989286

discriminant (Δ)

461293840196623428127703978572

Faltings height

4.4034

naive height

76.6493

primes of bad reduction

2, 223640842707413, 515663680448711

regulator

4967697386444.742649977456281874021817926756892984352235135565018

submitted by

Volkan Dagli

submitted at

2026-10-17 10:22:29 UTC

later contributions

(-37735, 9158448)
(-1806, 6623753)
(-177, 6295600)
(-37, 6266560)
(557, 6141840)
(2292, 5763173)
(56492, 8492685)
(124692, 40603973)
(-631661/25, 1178988577/125)
(-413012/9, 212912381/27)
(15745684/961, 29247194873/29791)
(959762629/17424, 18208243461517/2299968)
(16845344559906/1024960225, 30680473388418927859/32814101603375)

BASE records/rank_13.md#17 + Werr 4-Pillar Multi-Layer Algebraic Sieve conductor factorization.

last edited by Volkan Dagli at 2026-10-17 10:22:30 UTC · history