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curve #4382

y² = x³ + x² − 30762x + 2211409

a-invariants: [0, 1, 0, -30762, 2211409]
c-invariants: [1476592, -1919516896]
rank (lower bound): ≥ 4
torsion subgroup: ℤ/3ℤ
conductor (N): 100807996
discriminant (Δ): -269152913768176
Faltings height: 1.5142
naive height: 42.7507
primes of bad reduction: 2, 19, 43, 109, 283
regulator: 39.03097654847093835830898130762169809938482354
submitted by: Volkan Dagli
submitted at: 2026-10-17 10:09:30 UTC
last updated: 2026-10-17 10:09:30 UTC

Witness: 4 independent points log in to add more points →

(-30, 1763)
(-202, 473)
(314, 4859)
(-159, 1763)

Commentary

Curve from torsion/torsion_Z3.tsv.gz:30 (mrubinst/elliptic-curves-by-rank) + Werr 4-Pillar Algebraic Sieve factorization.

last edited by Volkan Dagli at 2026-10-17 10:09:30 UTC · history

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