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curve #42

y² + y = x³ − x

a-invariants: [0, 0, 1, -1, 0]
rank (lower bound): ≥ 1
conductor (N): 37 ★ record for rank ≥ 1
naive height: 11.6136 ★ record for rank ≥ 1
Faltings height: -0.9965 ★ record for rank ≥ 1
discriminant (Δ): 37 ★ record for rank ≥ 1
primes of bad reduction: 37
regulator: 0.05111140823996884023588609975694202160954
submitted by: David Renshaw
last updated: 2026-07-01 23:04:08

Witness: 1 independent points

(0, 0)

Commentary

The standard conductor 37 rank-one curve y^2 + y = x^3 - x, with generator [0, 0].

last edited by David Renshaw at 2026-05-28 04:36:54 · history

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