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curve #1524

y² + xy + y = x³ + x² + 12805x + 18204770

a-invariants: [1, 1, 1, 12805, 18204770]
rank (lower bound): ≥ 3
torsion subgroup: ℤ/4ℤ
conductor (N): 344955
discriminant (Δ): -143221166424194625
Faltings height: 1.9710
naive height: 46.9569
primes of bad reduction: 3, 5, 13, 29, 61
regulator: 7.6674077727667290324342568004056689372024671
submitted by: Michael Rubinstein
submitted at: 2026-09-25 00:49:40 UTC
last updated: 2026-09-25 00:49:40 UTC

Witness: 3 independent points log in to add more points →

(-2187/16, 243157/64)
(-232, 1793)
(988, 31073)

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 00:49:40 UTC · history

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