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curve #4333

y² + y = x³ − 76222578978x + 8414040694422908

a-invariants: [0, 0, 1, -76222578978, 8414040694422908]
c-invariants: [3658683790944, -7269731159981392728]
rank (lower bound): ≥ 7
torsion subgroup: ℤ/3ℤ
conductor (N): 61558727099937615
discriminant (Δ): -2241880988978779528068311194950075
Faltings height: 5.1632
naive height: 86.8605
primes of bad reduction: 3, 5, 37, 53, 61, 89, 163, 87589
regulator: 25125.62603148851347565964051017417470306927504450187
submitted by: Volkan Dagli
submitted at: 2026-10-17 10:05:15 UTC
last updated: 2026-10-17 10:05:15 UTC

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

(-139271/4, 840027831/8)
(-3240879/16, 7978922503/64)
(1356417/4, 1174688021/8)
(1533634/9, 521817184/27)
(110783913/256, 973356084757/4096)
(-79874, 118290567)
(163252329/784, 870089011819/21952)

Commentary

BASE torsion/torsion_Z3.tsv.gz:4784 (mrubinst/elliptic-curves-by-rank) + conductor prime factorization via pCwOrM Werr 4-Pillar Algebraic Sieve.

last edited by Volkan Dagli at 2026-10-17 10:05:15 UTC · history

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