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curve #4341

y² + xy + y = x³ − x² − 231181612151x + 17549469487990446

a-invariants: [1, -1, 1, -231181612151, 17549469487990446]
c-invariants: [11096717383233, -15162691702395521025]
rank (lower bound): ≥ 6
torsion subgroup: ℤ/4ℤ
conductor (N): 1456311062105757
discriminant (Δ): 657703000864423187930847157227675729
Faltings height: 5.5665
naive height: 90.1130
primes of bad reduction: 3, 11, 13, 29, 47, 191, 251, 17317
regulator: 5138.6779618576325996467273269367576419081028411533
submitted by: Volkan Dagli
submitted at: 2026-10-17 10:05:32 UTC
last updated: 2026-10-17 10:05:32 UTC

Witness: 6 independent points log in to add more points →

(-5905/4, 1070056311/8)
(878681, 701576535)
(-395724, 217140438)
(-26055529/100, 245275452651/1000)
(1921376, 2580991338)
(-44551432/121, 305952932598/1331)

Commentary

BASE torsion/torsion_Z4.tsv.gz:4259 (mrubinst/elliptic-curves-by-rank) + conductor prime factorization via pCwOrM Werr 4-Pillar Algebraic Sieve.

last edited by Volkan Dagli at 2026-10-17 10:05:32 UTC · history

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