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curve #4525

y² + xy + y = x³ − 909903650x + 10576401079872

a-invariants: [1, 0, 1, -909903650, 10576401079872]
c-invariants: [43675375177, -9138076046072389]
rank (lower bound): ≥ 6
torsion subgroup: ℤ/3ℤ
conductor (N): 53612129532302
discriminant (Δ): -111098771279243927707567996
Faltings height: 3.9037
naive height: 73.5025
primes of bad reduction: 2, 11, 37, 41, 61, 349, 1237
regulator: 1508.9109908864682210131132575395517852415809373746
submitted by: Volkan Dagli
submitted at: 2026-10-17 10:33:51 UTC
last updated: 2026-10-17 10:33:51 UTC

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

(31881, 3721947)
(-1493, 3454955)
(20196, 651416)
(12160, 1138496)
(65255, 15102481)
(429911/25, 14060269/125)

Commentary

BASE torsion/torsion_Z3.tsv.gz:512 + Werr Core & 4-Pillar Algebraic Sieve conductor factorization.

last edited by Volkan Dagli at 2026-10-17 10:33:51 UTC · history

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