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curve #4517

y² + xy = x³ + x² − 83696225x + 294602641125

a-invariants: [1, 1, 0, -83696225, 294602641125]
c-invariants: [4017418825, -254566812573125]
rank (lower bound): ≥ 7
torsion subgroup: ℤ/2ℤ
conductor (N): 60825818974350
discriminant (Δ): 20536925389404662250000
Faltings height: 3.2567
naive height: 66.3417
primes of bad reduction: 2, 3, 5, 41, 61, 241, 269
regulator: 2693.837075650373073517475200820501676094931464685400
submitted by: Volkan Dagli
submitted at: 2026-10-17 10:33:19 UTC
last updated: 2026-10-17 10:33:19 UTC

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

(6430, -152665)
(5005, -35815)
(7955, -367690)
(7055, 231710)
(5930, 79835)
(-7295, -715390)
(-890, 607395)

Commentary

BASE torsion/torsion_Z2.tsv.gz:315434 + Werr Core & 4-Pillar Algebraic Sieve conductor factorization.

last edited by Volkan Dagli at 2026-10-17 10:33:19 UTC · history

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