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curve #4326

y² + xy = x³ − x² − 62527117268706x + 190380882255193890296

a-invariants: [1, -1, 0, -62527117268706, 190380882255193890296]
c-invariants: [3001301628897897, -164489068762630191175221]
rank (lower bound): ≥ 8
torsion subgroup: ℤ/3ℤ
conductor (N): 664445408124925173258
discriminant (Δ): -12438953593000522083706789187501887167156
Faltings height: 6.6503
naive height: 106.9143
primes of bad reduction: 2, 3, 31, 37, 43, 79, 181, 197, 211, 773
regulator: 604396.669744952113173866477874423227288632659031360221
submitted by: Volkan Dagli
submitted at: 2026-10-17 10:04:55 UTC
last updated: 2026-10-17 10:04:55 UTC

Witness: 8 independent points log in to add more points →

(9786854, -22717147734)
(43006510/9, -22776764072/27)
(1023978314, -32766496948710)
(9394036, 20779982224)
(115685206/25, -45120652144/125)
(3891274, -2449893350)
(6470162, 7525419556)
(109687771/25, 88392076541/125)

Commentary

BASE torsion/torsion_Z3.tsv.gz:7097 (mrubinst/elliptic-curves-by-rank) + conductor prime factorization via pCwOrM Werr 4-Pillar Algebraic Sieve.

last edited by Volkan Dagli at 2026-10-17 10:04:55 UTC · history

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