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curve #1298

y² = x³ + x² − 397505x + 96310384

a-invariants: [0, 1, 0, -397505, 96310384]
rank (lower bound): ≥ 6
torsion subgroup: ℤ/2ℤ
conductor (N): 44968690156 ☆ record for ℤ/2ℤ torsion, rank ≥ 6
discriminant (Δ): 1709349850209872 ☆ record for ℤ/2ℤ torsion, rank ≥ 6
Faltings height: 1.9109
naive height: 50.2925
primes of bad reduction: 2, 13, 17, 43, 53, 101
regulator: 225.35585877746084606680698345878389637596018570133
submitted by: Michael Rubinstein
submitted at: 2026-09-24 17:27:53 UTC
last updated: 2026-09-24 17:27:53 UTC

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

(411, 1591)
(-191, 12857)
(325, 1247)
(385, 697)
(381, -559)
(9871, 978809)

Commentary

Torsion Z/2. From Michael Rubinstein's github repository: https://github.com/mrubinst/elliptic-curves-by-rank

last edited by Michael Rubinstein at 2026-09-24 17:27:53 UTC · history

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