curve #121

y² + y = x³ − 36673x + 2704878

a-invariants: [0, 0, 1, -36673, 2704878]
rank (lower bound): ≥ 7
conductor (N): 814434447535
naive height: 43.1443
Faltings height: 1.3530
discriminant (Δ): -4072172237675
primes of bad reduction: 5, 162886889507
regulator: 584.4980643050451293253654768401361089199857192260729
submitted by: David Renshaw
last updated: 2026-07-01 22:57:21

Witness: 7 independent points

(111, 42)
(106, 92)
(121, 197)
(86, 432)
(136, 482)
(109, 50)
(71, 677)

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 00:08:26 · history