curve #134

y² + xy + y = x³ − 1493028x + 701820182

a-invariants: [1, 0, 1, -1493028, 701820182]
rank (lower bound): ≥ 9
conductor (N): 72070075910145406
naive height: 54.2626
Faltings height: 2.2572
discriminant (Δ): 144140151820290812
primes of bad reduction: 2, 1187, 30358077468469
regulator: 58361.246530795783731326957120654161428495711241018202990
submitted by: David Renshaw
last updated: 2026-07-01 22:52:29

Witness: 9 independent points

(719, 37)
(729, 613)
(679, 763)
(731, 715)
(675, 961)
(665, 1441)
(745, 1401)
(659, 1723)
(688, 285)

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 00:08:42 · history