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curve #1362

y² + xy + y = x³ − 61882205936243x + 187448229579982169658

a-invariants: [1, 0, 1, -61882205936243, 187448229579982169658]
rank (lower bound): ≥ 8
torsion subgroup: ℤ/3ℤ
conductor (N): 669692943114425917310
discriminant (Δ): -12895789489877475465585417637556756909500
Faltings height: 6.6500
naive height: 106.8832
primes of bad reduction: 2, 5, 13, 37, 47, 97, 127, 241, 283, 367, 739
regulator: 238168.903647928945353930205889096673854879831582295126
submitted by: Michael Rubinstein
submitted at: 2026-09-24 17:38:51 UTC
last updated: 2026-09-24 17:38:51 UTC

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

(4986489, 1689460460)
(87984729, 822063085050)
(564772459/121, 722581798570/1331)
(1454909, -10025444170)
(6269589, 6772974350)
(4278989, 998940460)
(18272011/4, -2405685485/8)
(5288349, -2847088180)

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 17:38:51 UTC · history

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