curve #100

y² + y = x³ − 21078967x + 35688990786

a-invariants: [0, 0, 1, -21078967, 35688990786]
rank (lower bound): ≥ 10
torsion subgroup: trivial
conductor (N): 22630148490190627609
naive height: 62.2050
Faltings height: 3.1147
discriminant (Δ): 49175312669184233794357
primes of bad reduction: 41, 53, 10414242287248333
regulator: 283148.7940006095034539845739385244675957106444863463613555
submitted by: David Renshaw
submitted at: 2026-06-23 23:50:30 UTC
last updated: 2026-07-01 22:51:29 UTC

Witness: 10 independent points

(2190, 5432)
(17, 187964)
(-4329, 214040)
(2137, 20060)
(3091, 8135)
(3144, 22233)
(1872, 52814)
(1819, 58008)
(1944, 45366)
(3215, 33927)

Commentary

EW 2004 (Elkies-Watkins, ANTS-VI, arXiv:math/0403374) Table 2 low-conductor rank-10 list; this curve was absent from the leaderboard. Rank-10 witness via 10 independent rational points (Neron-Tate pairing).

last edited by David Renshaw at 2026-06-23 23:50:30 UTC · history