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curve #4456

y² + y = x³ − 1117x + 13026

a-invariants: [0, 0, 1, -1117, 13026]
c-invariants: [53616, -11254680]
rank (lower bound): ≥ 5
torsion subgroup: trivial
conductor (N): 53149343
discriminant (Δ): 15891653557
Faltings height: 0.6928
naive height: 32.6688
primes of bad reduction: 13, 23, 149, 1193
regulator: 7.70499352145395249014053486769522665316746511647
submitted by: Volkan Dagli
submitted at: 2026-10-17 10:24:43 UTC
last updated: 2026-10-17 10:24:43 UTC

Witness: 5 independent points log in to add more points →

(-9, 149)
(11, 45)
(14, 11)
(24, 6)
(37, 149)

Commentary

BASE records/rank_5.md#7 + Werr 4-Pillar Multi-Layer Algebraic Sieve conductor factorization.

last edited by Volkan Dagli at 2026-10-17 10:24:43 UTC · history

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