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curve #2037

y² + xy = x³ + x² − 309383x − 57492993

a-invariants: [1, 1, 0, -309383, -57492993]
rank (lower bound): ≥ 6
torsion subgroup: ℤ/2ℤ
conductor (N): 146635526910
discriminant (Δ): 473716187534111790
Faltings height: 2.1169
naive height: 49.5406
primes of bad reduction: 2, 3, 5, 17, 89, 769, 4201
regulator: 17333.909405300388814864788229749968316633394097312
submitted by: Steps Unbounded
submitted at: 2026-09-26 05:05:13 UTC
last updated: 2026-09-26 05:05:13 UTC

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

(-413, 431)
(-393, 2091)
(-341, 3086)
(643, -3474)
(-1253/4, 24993/8)
(-1169/4, 23895/8)

Commentary

2-isogenous partner of curve#1236 (Michael Rubinstein).

last edited by Steps Unbounded at 2026-09-26 21:49:08 UTC · history

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