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curve #1302

y² + xy = x³ − 3915438x + 3702705367

a-invariants: [1, 0, 0, -3915438, 3702705367]
rank (lower bound): ≥ 6
torsion subgroup: ℤ/2ℤ
conductor (N): 82820649775
discriminant (Δ): -2082096900544319921875
Faltings height: 2.8039
naive height: 57.5880
primes of bad reduction: 5, 29, 71, 109, 509
regulator: 514.66523411467421619957557222283505593282191755484
submitted by: Michael Rubinstein
submitted at: 2026-09-24 17:28:34 UTC
last updated: 2026-09-24 17:28:34 UTC

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

(1607, 38709)
(1062, 26719)
(-1663, 75769)
(-1438, 80469)
(41517/16, 6634091/64)
(77683/9, 21022663/27)

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 17:28:34 UTC · history

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