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curve #2068

y² + xy + y = x³ + x² − 15333290x + 22065838247

a-invariants: [1, 1, 1, -15333290, 22065838247]
rank (lower bound): ≥ 2
torsion subgroup: ℤ/2ℤ × ℤ/4ℤ
conductor (N): 308490
discriminant (Δ): 20257268493733779690000
Faltings height: 3.0384
naive height: 61.2502
primes of bad reduction: 2, 3, 5, 7, 13, 113
regulator: 21.3754015138646139883394520396656392863133
submitted by: Steps Unbounded
submitted at: 2026-09-26 05:13:08 UTC
last updated: 2026-09-26 05:13:08 UTC

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

(6339/4, -340963/8)
(306273/289, 408672623/4913)

Commentary

2-isogenous partner of curve#1181 (David Renshaw), curve#2637 (Natanael Wildner Fraga).

last edited by Steps Unbounded at 2026-09-26 21:56:15 UTC · history

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