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curve #1339

y² + xy = x³ − x² − 2346023850x + 12480379081640036

a-invariants: [1, -1, 0, -2346023850, 12480379081640036]
rank (lower bound): ≥ 7
torsion subgroup: ℤ/3ℤ
conductor (N): 33696840882516030
discriminant (Δ): -67287427693801602746701454437978800
Faltings height: 5.3617
naive height: 87.6490
primes of bad reduction: 2, 3, 5, 37, 53, 61, 163, 233, 9157
regulator: 18335.26638309335522512868752126847470019477195770176
submitted by: Michael Rubinstein
submitted at: 2026-09-24 17:34:52 UTC
last updated: 2026-09-24 17:34:52 UTC

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

(639323, 521497536)
(-77552, 110473786)
(-51797, 111663376)
(3198428, 5718951546)
(-135272, 101667046)
(-235172, 5183626)
(688348, -580878614)

Commentary

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

last edited by Michael Rubinstein at 2026-09-24 17:34:52 UTC · history

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