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curve #1398

y² + xy = x³ + 175871926195x − 19454670108832623

a-invariants: [1, 0, 0, 175871926195, -19454670108832623]
rank (lower bound): ≥ 2
torsion subgroup: ℤ/10ℤ
conductor (N): 18916590
discriminant (Δ): -511657929046009691841682710000000000
Faltings height: 5.5395
naive height: 89.2927
primes of bad reduction: 2, 3, 5, 7, 11, 19, 431
regulator: 27.9411062783053630004067181947265103317435
submitted by: Michael Rubinstein
submitted at: 2026-09-24 23:21:01 UTC
last updated: 2026-09-24 23:21:01 UTC

Witness: 2 independent points log in to add more points →

(32969374/121, 293529622193/1331)
(107984554/841, 1764609576467/24389)

Commentary

Torsion Z/10. From Michael Rubinstein's github repository: https://github.com/mrubinst/elliptic-curves-by-rank

last edited by Michael Rubinstein at 2026-09-24 23:21:01 UTC · history

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