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curve #4459

y² + xy = x³ − x² − 34x + 64

a-invariants: [1, -1, 0, -34, 64]
c-invariants: [1641, -47925]
rank (lower bound): ≥ 4
torsion subgroup: trivial
conductor (N): 614066
discriminant (Δ): 1228132
Faltings height: -0.1243
naive height: 22.2092
primes of bad reduction: 2, 307033
regulator: 21.22549118520972037736431059618969688069510816
submitted by: Volkan Dagli
submitted at: 2026-10-17 10:24:53 UTC
last updated: 2026-10-17 10:24:53 UTC

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

(-6, 8)
(-5, 12)
(-3, 13)
(19, 68)

Commentary

BASE records/rank_4.md#5 + Werr 4-Pillar Multi-Layer Algebraic Sieve conductor factorization.

last edited by Volkan Dagli at 2026-10-17 10:24:54 UTC · history

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