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curve #4357

y² = x³ − x² − 242660383x + 1336936648012

a-invariants: [0, -1, 0, -242660383, 1336936648012]
c-invariants: [11647698400, -1155043377692000]
rank (lower bound): ≥ 5
torsion subgroup: ℤ/4ℤ
conductor (N): 101769397800
discriminant (Δ): 142421857096345427711250000
Faltings height: 3.7580
naive height: 69.5351
primes of bad reduction: 2, 3, 5, 7, 31, 71, 101, 109
regulator: 405.441563046025393611440936489344364708349907845
submitted by: Volkan Dagli
submitted at: 2026-10-17 10:06:07 UTC
last updated: 2026-10-17 10:06:07 UTC

Witness: 5 independent points log in to add more points →

(55032, 12435650)
(12787, 569775)
(231217/16, 58931775/64)
(-8797, 1670559)
(11291, 190743)

Commentary

BASE torsion/torsion_Z4.tsv.gz:2317 (mrubinst/elliptic-curves-by-rank) + conductor prime factorization via pCwOrM Werr 4-Pillar Algebraic Sieve.

last edited by Volkan Dagli at 2026-10-17 10:06:07 UTC · history

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