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curve #4457

y² + y = x³ − 2037x + 35806

a-invariants: [0, 0, 1, -2037, 35806]
c-invariants: [97776, -30936600]
rank (lower bound): ≥ 5
torsion subgroup: trivial
conductor (N): 53155881
discriminant (Δ): -12916879083
Faltings height: 0.7465
naive height: 34.4949
primes of bad reduction: 3, 421, 14029
regulator: 101.654283913693310795757220942077724297204066064
submitted by: Volkan Dagli
submitted at: 2026-10-17 10:24:46 UTC
last updated: 2026-10-17 10:24:46 UTC

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

(-50, 112)
(-47, 166)
(-29, 265)
(-11, 238)
(88, 733)

Commentary

BASE records/rank_5.md#8 + Werr 4-Pillar Multi-Layer Algebraic Sieve conductor factorization.

last edited by Volkan Dagli at 2026-10-17 10:24:46 UTC · history

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