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curve #1347

y² = x³ + x² − 1894949065x + 31743132642039

a-invariants: [0, 1, 0, -1894949065, 31743132642039]
rank (lower bound): ≥ 8
torsion subgroup: ℤ/2ℤ
conductor (N): 29231074244902976
discriminant (Δ): 172435824354756691963645952
Faltings height: 4.0259
naive height: 75.7010
primes of bad reduction: 2, 17, 73, 89, 137, 257, 457
regulator: 27173.9561341275043301670401132706842751403452358509094
submitted by: Michael Rubinstein
submitted at: 2026-09-24 17:36:17 UTC
last updated: 2026-09-24 17:36:17 UTC

Witness: 8 independent points log in to add more points →

(7367, 4264144)
(29807, 1320424)
(-14869, 7525424)
(34771, -2809624)
(6082, 4521401)
(662717, -538365656)
(24329, -204572)
(24586, -126701)

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 17:36:18 UTC · history

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