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curve #4377

y² + xy + y = x³ + x² − 1049984x + 993633770

a-invariants: [1, 1, 1, -1049984, 993633770]
c-invariants: [50399233, -858877571681]
rank (lower bound): ≥ 4
torsion subgroup: ℤ/4ℤ
conductor (N): 204122451
discriminant (Δ): -352808138863346323833
Faltings height: 2.6300
naive height: 54.9578
primes of bad reduction: 3, 13, 17, 37, 53, 157
regulator: 191.9083231821227459340530962909442030070660897
submitted by: Volkan Dagli
submitted at: 2026-10-17 10:06:49 UTC
last updated: 2026-10-17 10:06:49 UTC

Witness: 4 independent points log in to add more points →

(-986, 33227)
(-690, 37630)
(-1300, 13445)
(9804, 961102)

Commentary

BASE torsion/torsion_Z4.tsv.gz:11 (mrubinst/elliptic-curves-by-rank) + conductor prime factorization via pCwOrM Werr 4-Pillar Algebraic Sieve.

last edited by Volkan Dagli at 2026-10-17 10:06:49 UTC · history

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