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curve #1301

y² + xy = x³ − 4172813x + 3280352992

a-invariants: [1, 0, 0, -4172813, 3280352992]
rank (lower bound): ≥ 6
torsion subgroup: ℤ/2ℤ
conductor (N): 82820649775
discriminant (Δ): 532899118396015625
Faltings height: 2.4573
naive height: 57.3459
primes of bad reduction: 5, 29, 71, 109, 509
regulator: 514.66523411467421619957557222283505593282191755484
submitted by: Michael Rubinstein
submitted at: 2026-09-24 17:28:23 UTC
last updated: 2026-09-24 17:28:23 UTC

Witness: 6 independent points log in to add more points →

(1317, 7679)
(11467, 1203929)
(5043/4, 34007/8)
(1243, 3177)
(-887, 79715)
(4543/4, 15757/8)

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 17:28:24 UTC · history

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