curve #127

y² + y = x³ − 15577x + 744876

a-invariants: [0, 0, 1, -15577, 744876]
c-invariants: [747696, -643573080]
rank (lower bound): ≥ 7
torsion subgroup: trivial
conductor (N): 2206378706437
discriminant (Δ): 2206378706437
Faltings height: 1.2134
naive height: 40.5743
primes of bad reduction: 2206378706437
regulator: 1153.178388687324427112843454112369052995943965950190
submitted by: David Renshaw
submitted at: 2026-06-24 00:08:33 UTC
last updated: 2026-07-01 22:57:20 UTC

Witness: 7 independent points log in to add more points →

(68, 8)
(76, 0)
(67, 44)
(77, 44)
(66, 65)
(78, 66)
(63, 116)

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 00:08:33 UTC · history