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curve #2042

y² = x³ − x² + 15935x + 3256321

a-invariants: [0, -1, 0, 15935, 3256321]
rank (lower bound): ≥ 5
torsion subgroup: ℤ/2ℤ
conductor (N): 232106304 ☆ record for ℤ/2ℤ torsion, rank ≥ 5
discriminant (Δ): -4854668607848448
Faltings height: 1.6909
naive height: 43.5186
primes of bad reduction: 2, 3, 17, 47, 89
regulator: 859.329314206862385221394854116900862492162459622
submitted by: Steps Unbounded
submitted at: 2026-09-26 05:07:06 UTC
last updated: 2026-09-26 05:07:06 UTC

Witness: 5 independent points log in to add more points →

(31, 1944)
(211, 3996)
(-32, 1647)
(83, 2268)
(-97, 888)

Commentary

2-isogenous partner of curve#1272 (Michael Rubinstein).

last edited by Steps Unbounded at 2026-09-26 21:50:16 UTC · history

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