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curve #1361

y² + xy + y = x³ − 28403376865544x + 58189065087724781826

a-invariants: [1, 0, 1, -28403376865544, 58189065087724781826]
rank (lower bound): ≥ 8
torsion subgroup: ℤ/3ℤ
conductor (N): 53669457456992966810
discriminant (Δ): 3788467181511577571452141674694036096100
Faltings height: 6.4951
naive height: 104.5462
primes of bad reduction: 2, 5, 13, 23, 31, 37, 61, 103, 127, 163, 120319
regulator: 66982.7700322788785460553669126101310899817476560439751
submitted by: Michael Rubinstein
submitted at: 2026-09-24 17:38:41 UTC
last updated: 2026-09-24 17:38:41 UTC

Witness: 8 independent points log in to add more points →

(-5372555, -7461393283)
(50688453/16, -2946036603/64)
(-1575427, -9950410687)
(25026589/9, 22694079359/27)
(-11935745/9, -261094507241/27)
(-3549724, 10692180646)
(353296791/121, -515434582409/1331)
(10521527/4, -10369555931/8)

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 17:38:41 UTC · history

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