curve #1456

y² + xy = x³ − 29238170078929270129980x + 1924302723749877479432872761104400

a-invariants: [1, 0, 0, -29238170078929270129980, 1924302723749877479432872761104400]
rank (lower bound): ≥ 2
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 386090160017430
discriminant (Δ): 8181403930537949069649408733014448930732270424064000000000000
Faltings height: 11.3419
naive height: 166.8029
primes of bad reduction: 2, 3, 5, 11, 23, 47, 503, 1031, 2087
regulator: 318.064501012706295904187595938649665572490
submitted by: Michael Rubinstein
submitted at: 2026-09-25 00:00:19 UTC
last updated: 2026-09-25 00:00:19 UTC

(35704790960360/361, 683241924852308780/6859)
(661645295465531506971974266040/6713948805400703689, 1647985120333524114969911693460679721111660/17396706561233928830681290363)

Torsion Z/6+Z/2. From Michael Rubinstein's github repository: https://github.com/mrubinst/elliptic-curves-by-rank

last edited by Michael Rubinstein at 2026-09-25 00:00:19 UTC · history