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curve #1295

y² + xy = x³ − 83296293x + 293440629889

a-invariants: [1, 0, 0, -83296293, 293440629889]
rank (lower bound): ≥ 5
torsion subgroup: ℤ/3ℤ
conductor (N): 8306144278
discriminant (Δ): -212486192299280085188608
Faltings height: 3.3410
naive height: 66.3331
primes of bad reduction: 2, 31, 43, 47, 151, 439
regulator: 158.360413149130242080422035798440778596826442578
submitted by: Michael Rubinstein
submitted at: 2026-09-24 17:27:22 UTC
last updated: 2026-09-24 17:27:22 UTC

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

(2866, 278311)
(6786, 198343)
(143074/25, 7731083/125)
(-1670, 654967)
(231474, 111165223)

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 17:27:22 UTC · history

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