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curve #1370

y² = x³ − x² − 29090496521x + 1015961393728521

a-invariants: [0, -1, 0, -29090496521, 1015961393728521]
rank (lower bound): ≥ 9
torsion subgroup: ℤ/2ℤ
conductor (N): 2816328834972349120320
discriminant (Δ): 1129662110147156052749892883353600
Faltings height: 5.0395
naive height: 83.8946
primes of bad reduction: 2, 3, 5, 13, 41, 61, 71, 181, 2521, 2785129
regulator: 389289.54453130096297426102784888170624734972196051812379
submitted by: Michael Rubinstein
submitted at: 2026-09-24 17:40:16 UTC
last updated: 2026-09-24 17:40:16 UTC

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(-158467, -40576224)
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(31073, 11917776)
(-91899, -53974200)

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 17:40:16 UTC · history

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