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curve #3434

y² + xy = x³ − 22297742x + 98226074116

a-invariants: [1, 0, 0, -22297742, 98226074116]
rank (lower bound): ≥ 5
torsion subgroup: ℤ/3ℤ
conductor (N): 2464716938 ☆ record for ℤ/3ℤ torsion, rank ≥ 5
discriminant (Δ): -3458733205462984211562496
Faltings height: 3.3957
naive height: 64.1443
primes of bad reduction: 2, 23, 31, 101, 109, 157
regulator: 90.7779029507172967795816327118897588470558182475
submitted by: Michael Rubinstein
submitted at: 2026-09-27 05:31:03 UTC
last updated: 2026-09-27 05:31:03 UTC

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

(-6020, 122594)
(21452, -3091630)
(85436/25, 30896026/125)
(13372, 1473570)
(372124, 226798914)

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 05:31:03 UTC · history

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