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curve #4458

y² + y = x³ + x² − 22x + 50

a-invariants: [0, 1, 1, -22, 50]
c-invariants: [1072, -49816]
rank (lower bound): ≥ 4
torsion subgroup: trivial
conductor (N): 723211
discriminant (Δ): -723211
Faltings height: -0.1731
naive height: 21.6322
primes of bad reduction: 73, 9907
regulator: 4.166513949745202064577963756999196877315050496
submitted by: Volkan Dagli
submitted at: 2026-10-17 10:24:49 UTC
last updated: 2026-10-17 10:24:49 UTC

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

(-1, 8)
(1, 5)
(3, 4)
(4, 6)

Commentary

BASE records/rank_4.md#7 + Werr 4-Pillar Multi-Layer Algebraic Sieve conductor factorization.

last edited by Volkan Dagli at 2026-10-17 10:24:49 UTC · history

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