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curve #1335

y² + xy + y = x³ − 810107314098x + 278171511728355256

a-invariants: [1, 0, 1, -810107314098, 278171511728355256]
rank (lower bound): ≥ 7
torsion subgroup: ℤ/3ℤ
conductor (N): 10190734612809870
discriminant (Δ): 597831598737219445255023033023437500
Faltings height: 5.6827
naive height: 93.8749
primes of bad reduction: 2, 3, 5, 7, 17, 29, 31, 2659, 5503
regulator: 2235.684748400992552047742497887137251355137612970086
submitted by: Michael Rubinstein
submitted at: 2026-09-24 17:34:11 UTC
last updated: 2026-09-24 17:34:11 UTC

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

(-720205, 698964477)
(307445, -241335273)
(1506455/4, -1303618059/8)
(1064795, -789725523)
(-1000705, 295006227)
(24733895, -122941559523)
(3023045, -5046924273)

Commentary

Torsion Z/3. From Michael Rubinstein's github repository: https://github.com/mrubinst/elliptic-curves-by-rank

last edited by Michael Rubinstein at 2026-09-24 17:34:11 UTC · history

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