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curve #1479

y² + xy + y = x³ − x² − 11700269717099x + 15404301420820828859

a-invariants: [1, -1, 1, -11700269717099, 15404301420820828859]
rank (lower bound): ≥ 2
torsion subgroup: ℤ/9ℤ
conductor (N): 52712478
discriminant (Δ): -941629261925919531418245981536256
Faltings height: 5.9432
naive height: 101.8855
primes of bad reduction: 2, 3, 7, 13, 17, 631
regulator: 49.7698717318076939956745683244772893322515
submitted by: Michael Rubinstein
submitted at: 2026-09-25 00:23:18 UTC
last updated: 2026-09-25 00:23:18 UTC

Witness: 2 independent points log in to add more points →

(20927608827/10609, 4877881595590/1092727)
(7347872979/3721, -331586257454/226981)

Commentary

Torsion Z/9. From Michael Rubinstein's github repository: https://github.com/mrubinst/elliptic-curves-by-rank

last edited by Michael Rubinstein at 2026-09-25 00:23:19 UTC · history

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