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curve #1731

y² + xy = x³ + 676455x + 12569549337

a-invariants: [1, 0, 0, 676455, 12569549337]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/10ℤ
conductor (N): 140910
discriminant (Δ): -68272420831874513100000
Faltings height: 3.0604
naive height: 60.0322
primes of bad reduction: 2, 3, 5, 7, 11, 61
regulator: 3.970073423704288975241127699224308196476
submitted by: hdeping
submitted at: 2026-09-25 10:32:53 UTC
last updated: 2026-09-25 10:32:53 UTC

Witness: 1 independent point log in to add more points →

(-336, 111093)

Commentary

Specialization u=-5/2 of the X_1(10) universal curve for torsion Z/10Z (Halbeisen-Hungerbuehler-Voznyy-Zargar 2021, Thm 4), y^2+xy=x^3+A(u)x^2+B(u)x.

last edited by hdeping at 2026-09-27 08:50:23 UTC · history

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