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curve #1348

y² = x³ + x² − 677920785x + 6446025754639

a-invariants: [0, 1, 0, -677920785, 6446025754639]
rank (lower bound): ≥ 8
torsion subgroup: ℤ/2ℤ
conductor (N): 31226965890509248
discriminant (Δ): 1988219811065421206264102912
Faltings height: 3.9920
naive height: 72.6172
primes of bad reduction: 2, 17, 23, 31, 71, 577, 593, 1657
regulator: 19447.4522447273999485469145244588114849515690249404624
submitted by: Michael Rubinstein
submitted at: 2026-09-24 17:36:28 UTC
last updated: 2026-09-24 17:36:28 UTC

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

(-12079, 3587816)
(18419, 456688)
(18810, 591583)
(2507, 2182256)
(20595, 1104592)
(-21565, 3322208)
(109131, 35102416)
(17867, 193936)

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 17:36:28 UTC · history

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