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curve #1657

y² + y = x³ + x² + 755369674600x + 1108437052817940098

a-invariants: [0, 1, 1, 755369674600, 1108437052817940098]
rank (lower bound): ≥ 5
torsion subgroup: ℤ/5ℤ
conductor (N): 11277313955817
discriminant (Δ): -558353172065255258963434938348960014811
Faltings height: 6.1158 ☆ record for ℤ/5ℤ torsion, rank ≥ 5
naive height: 96.6221 ☆ record for ℤ/5ℤ torsion, rank ≥ 5
primes of bad reduction: 3, 7, 13, 23, 107, 659, 25471
regulator: 1714.03653142782501794595568909688208828265779816
submitted by: Michael Rubinstein
submitted at: 2026-09-25 02:31:30 UTC
last updated: 2026-09-25 02:31:30 UTC

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

(-3103187/4, 1884722927/8)
(-664169, 560148049)
(6334147, 16125385594)
(63378862, 504612999754)
(22337407, 105657223990)

Commentary

Torsion Z/5. From Michael Rubinstein's github repository: https://github.com/mrubinst/elliptic-curves-by-rank

last edited by Michael Rubinstein at 2026-09-25 02:31:30 UTC · history

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