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curve #4497

y² + y = x³ + x² − 842x + 3192

a-invariants: [0, 1, 1, -842, 3192]
c-invariants: [40432, -3000664]
rank (lower bound): ≥ 6
torsion subgroup: trivial
conductor (N): 33039404549
discriminant (Δ): 33039404549
Faltings height: 0.7112
naive height: 31.8221
primes of bad reduction: 1117, 1123, 26339
regulator: 253.96429050853577324015793742302562152627339429091
submitted by: Volkan Dagli
submitted at: 2026-10-17 10:31:32 UTC
last updated: 2026-10-17 10:31:32 UTC

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

(0, 56)
(1, 48)
(3, 26)
(27, 29)
(-10, 103)
(-30, -49)

Commentary

BASE records/rank_6.md#19 + Werr 4-Pillar Multi-Layer Algebraic Sieve conductor factorization.

last edited by Volkan Dagli at 2026-10-17 10:31:33 UTC · history

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