curve #3077

y² + xy = x³ − 681179687329862935396x + 6877345661595357821090874031376

a-invariants: [1, 0, 0, -681179687329862935396, 6877345661595357821090874031376]
rank (lower bound): ≥ 9
torsion subgroup: ℤ/3ℤ
conductor (N): 574681033331622196154685510
discriminant (Δ): -204122221751241718177893044928344354530298886415319084256460800
Faltings height: 10.7971
naive height: 155.5347
primes of bad reduction: 2, 3, 5, 7, 11, 13, 19, 43, 67, 97, 3604150670923399
regulator: 1082322.7596832676099346188435553218745557711439123684378
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:36:09 UTC
last updated: 2026-09-26 20:36:09 UTC

Witness: 9 independent points log in to add more points →

(2458097096, 2284247502195932)
(-3345689464, -3019751781976228)
(18104595656, 692177157469532)
(16699524296, 398782230906332)
(-5852418754, -3265490050886518)
(8383466546, 1325103209028872)
(13533349856, 370609954059332)
(15986794850, 270791853120776)
(22090509896, 1615445801268572)

Commentary

Eroshkin - Siddiq - Voznyy (2023). Source: https://dujella.github.io/tors/z3old891011121314.html (curve entry 53). Published independent points; exact point coordinates checked.

last edited by Natanael Wildner Fraga at 2026-09-26 20:36:09 UTC · history