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curve #3461

y² + y = x³ + x² − 30379967x + 64440778455

a-invariants: [0, 1, 1, -30379967, 64440778455]
rank (lower bound): ≥ 5
torsion subgroup: ℤ/3ℤ
conductor (N): 27716849069
discriminant (Δ): 385828544822993909 ☆ record for ℤ/3ℤ torsion, rank ≥ 5
Faltings height: 2.7926
naive height: 63.3015
primes of bad reduction: 7, 13, 41, 223, 4759
regulator: 447.881314389693862415454133049511767725812488998
submitted by: Michael Rubinstein
submitted at: 2026-09-27 05:41:06 UTC
last updated: 2026-09-27 05:41:06 UTC

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

(12517/4, 41037/8)
(3565, 38174)
(1479, 150818)
(32561/16, 6726961/64)
(62409/16, 4659987/64)

Commentary

Torsion Z/3. From Michael Rubinstein's github repository: https://github.com/mrubinst/elliptic-curves-by-rank

last edited by Michael Rubinstein at 2026-09-27 05:41:06 UTC · history

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