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curve #1646

y² + xy + y = x³ − x² − 626261738x + 154278425976617

a-invariants: [1, -1, 1, -626261738, 154278425976617]
rank (lower bound): ≥ 5
torsion subgroup: ℤ/4ℤ
conductor (N): 239117376330
discriminant (Δ): -10266651044711154855834063667200
Faltings height: 4.6297
naive height: 78.8627
primes of bad reduction: 2, 3, 5, 7, 19, 29, 41, 53, 317
regulator: 179.670720559919159105501640074100871483626526802
submitted by: Michael Rubinstein
submitted at: 2026-09-25 02:21:19 UTC
last updated: 2026-09-25 02:21:19 UTC

Witness: 5 independent points log in to add more points →

(-2415, 12482263)
(-48335, 8487223)
(172977, 72174007)
(-50463, 7599847)
(-43743, 9919927)

Commentary

Torsion Z/4. From Michael Rubinstein's github repository: https://github.com/mrubinst/elliptic-curves-by-rank

last edited by Michael Rubinstein at 2026-09-25 02:21:19 UTC · history

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