curve #2833

y² + xy = x³ − 713603864890201881215581682056x + 173565939028395978646185524923160350368249920

a-invariants: [1, 0, 0, -713603864890201881215581682056, 173565939028395978646185524923160350368249920]
rank (lower bound): ≥ 5
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 44066485454258113056210
discriminant (Δ): 10242827087724374425960775981922615428569611771559584293144905107074164608849874366017638400
Faltings height: 16.1728
naive height: 217.8340
primes of bad reduction: 2, 3, 5, 7, 11, 13, 19, 23, 41, 47, 107, 151, 157, 467, 1471
regulator: 124823.925978897678087492750814363770206662972313
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:24:30 UTC
last updated: 2026-09-26 20:24:30 UTC

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

(783905935534154, 9792063060958885627490)
(46479406191344, 11853204869518918689560)
(-151796825230624, -16685052990404966422360)
(421910501388963328/81, 270592897898471141215286344/729)
(88151709135339248/121, 8455013912276220192150856/1331)

Commentary

Dujella - Peral (2021). Source: https://dujella.github.io/tors/z2z6old5.html (curve entry 45). Published independent points; exact point coordinates checked.

last edited by Natanael Wildner Fraga at 2026-09-26 20:24:30 UTC · history