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curve #1317

y² + xy = x³ − 2970385626x + 62367892354980

a-invariants: [1, 0, 0, -2970385626, 62367892354980]
rank (lower bound): ≥ 6
torsion subgroup: ℤ/3ℤ
conductor (N): 19402232256030
discriminant (Δ): -3057207159354645138505934400
Faltings height: 4.1909
naive height: 77.0513
primes of bad reduction: 2, 3, 5, 13, 59, 83, 499, 20359
regulator: 762.07573987249229479760294496634759800297687920377
submitted by: Michael Rubinstein
submitted at: 2026-09-24 17:31:07 UTC
last updated: 2026-09-24 17:31:07 UTC

Witness: 6 independent points log in to add more points →

(36948, 1730286)
(-31020, 11180670)
(1848, 7541286)
(-9072, 9415626)
(1741422/49, -452040282/343)
(2501908/81, 205188814/729)

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 17:31:07 UTC · history

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