curve #132

y² + xy = x³ − x² − 613069x + 98885089

a-invariants: [1, -1, 0, -613069, 98885089]
rank (lower bound): ≥ 9
conductor (N): 43537345103385386
naive height: 51.5923
Faltings height: 2.3474
discriminant (Δ): 10536037515019263412
primes of bad reduction: 2, 11, 179906384724733
regulator: 28128.954293126579199618116289534715658074636283516753699
submitted by: David Renshaw
last updated: 2026-07-01 22:52:28

Witness: 9 independent points

(168, 697)
(102, 6065)
(36, 8749)
(-52, 11455)
(-184, 14425)
(-228, 15173)
(740, 6703)
(806, 10905)
(157, 2468)

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 00:08:39 · history