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curve #4514

y² = x³ + x² − 11969049x + 8440997671

a-invariants: [0, 1, 0, -11969049, 8440997671]
c-invariants: [574514368, -7296469073920]
rank (lower bound): ≥ 7
torsion subgroup: ℤ/2ℤ
conductor (N): 955169876572096
discriminant (Δ): 78929186643580052639744
Faltings height: 3.0907
naive height: 60.5071
primes of bad reduction: 2, 23, 41, 73, 257, 769, 1097
regulator: 11138.89143847090751491423756369014058208859245278924
submitted by: Volkan Dagli
submitted at: 2026-10-17 10:33:12 UTC
last updated: 2026-10-17 10:33:12 UTC

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

(-2619, 147752)
(-2337, 153800)
(18426, 2458493)
(-799, 132268)
(142235, 53626984)
(-14731/4, 406801/8)
(3522, 99935)

Commentary

BASE torsion/torsion_Z2.tsv.gz:315884 + Werr Core & 4-Pillar Algebraic Sieve conductor factorization.

last edited by Volkan Dagli at 2026-10-17 10:33:12 UTC · history

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