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curve #1367

y² = x³ − x² − 11578096525x + 322133502806446

a-invariants: [0, -1, 0, -11578096525, 322133502806446]
rank (lower bound): ≥ 9
torsion subgroup: ℤ/2ℤ
conductor (N): 1541137965099140472324
discriminant (Δ): 54504961092793222771001818270032
Faltings height: 4.7935
naive height: 81.1307
primes of bad reduction: 2, 3, 13, 17, 31, 71, 73, 83, 373, 3877, 30133
regulator: 229246.60200025740311989289892968172322417360292118561328
submitted by: Michael Rubinstein
submitted at: 2026-09-24 17:39:43 UTC
last updated: 2026-09-24 17:39:43 UTC

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

(-82049, 26827989)
(-37177, -26479947)
(218031, -90345749)
(-72801, 27913813)
(103574, -15298062)
(2405081, -3726185151)
(-1030535/9, 326890603/27)
(578251, 432410661)
(2255419/25, 430605903/125)

Commentary

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

last edited by Michael Rubinstein at 2026-09-24 17:39:43 UTC · history

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