curve #114

y² + xy = x³ − x² − 16249x + 799549

a-invariants: [1, -1, 0, -16249, 799549]
rank (lower bound): ≥ 6
conductor (N): 6601024978
naive height: 40.7010
Faltings height: 1.1951
discriminant (Δ): 1214588595952
primes of bad reduction: 2, 23, 1543, 93001
regulator: 65.565732131126563160853854716322922008539638659313
submitted by: David Renshaw
last updated: 2026-07-01 22:59:17

Witness: 6 independent points

(78, 7)
(55, 237)
(-14, 1019)
(101, 375)
(-106, 1203)
(62, 135)

Commentary

From the tables of Elkies-Watkins 2004, 'Elliptic curves of large rank and small conductor' (ANTS-VI, arXiv:math/0403374): a low-conductor / low-discriminant curve of this rank that was absent from the leaderboard. Witness: a maximal independent set of rational points (Neron-Tate height pairing).

last edited by David Renshaw at 2026-06-24 00:08:17 · history