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curve #1331

y² = x³ + x² − 5594735x + 5089624849

a-invariants: [0, 1, 0, -5594735, 5089624849]
rank (lower bound): ≥ 7
torsion subgroup: ℤ/2ℤ
conductor (N): 49159219350656
discriminant (Δ): 8902832942842502912 ☆ record for ℤ/2ℤ torsion, rank ≥ 7
Faltings height: 2.5929 ☆ record for ℤ/2ℤ torsion, rank ≥ 7
naive height: 58.2256 ☆ record for ℤ/2ℤ torsion, rank ≥ 7
primes of bad reduction: 2, 23, 31, 41, 47, 71, 127
regulator: 4353.856817995033293313482547666978696619436870492904
submitted by: Michael Rubinstein
submitted at: 2026-09-24 17:33:30 UTC
last updated: 2026-09-24 17:33:30 UTC

Witness: 7 independent points log in to add more points →

(1089, 17018)
(1297, 4094)
(327, 57404)
(7047, -561844)
(4264, 242443)
(2769, -104098)
(9309/4, 547243/8)

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 17:33:30 UTC · history

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