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curve #4518

y² + xy = x³ − x² − 22563774x + 9921312324

a-invariants: [1, -1, 0, -22563774, 9921312324]
c-invariants: [1083061161, -8567140072725]
rank (lower bound): ≥ 7
torsion subgroup: ℤ/2ℤ
conductor (N): 83634450654222
discriminant (Δ): 692741964884464895851152
Faltings height: 3.2654
naive height: 62.4092
primes of bad reduction: 2, 3, 13, 61, 107, 199, 347
regulator: 4230.518978314594165459541691225859710216285925383079
submitted by: Volkan Dagli
submitted at: 2026-10-17 10:33:24 UTC
last updated: 2026-10-17 10:33:24 UTC

Witness: 7 independent points log in to add more points →

(4560, 40542)
(-744, 162534)
(5392, 209438)
(4596, 55014)
(-2369, 224960)
(-2568, 226950)
(-1784, 211830)

Commentary

BASE torsion/torsion_Z2.tsv.gz:315437 + Werr Core & 4-Pillar Algebraic Sieve conductor factorization.

last edited by Volkan Dagli at 2026-10-17 10:33:24 UTC · history

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