curve #2846

y² + xy = x³ − x² − 725725749888808798467228522840x + 237914533611148516496229543972918686770176000

a-invariants: [1, -1, 0, -725725749888808798467228522840, 237914533611148516496229543972918686770176000]
rank (lower bound): ≥ 5
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 967072153229620868430
discriminant (Δ): 9679490605955255900642793295841997747586006486914185524641592639748982831007382970638400
Faltings height: 15.8745
naive height: 217.8845
primes of bad reduction: 2, 3, 5, 7, 11, 13, 53, 151, 227, 733, 1367, 5897
regulator: 928269.057526345288275723459522466280434657763903
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:25:03 UTC
last updated: 2026-09-26 20:25:03 UTC

(802075139061645, 13108110167152346053620)
(1186620595911207/4, 55846173364895457747747/8)
(531208742642688, 1516773542115084783744)
(180507989444005605/361, 1567045258450190238510165/6859)
(12440798197833519/25, 6341623292913960894462/125)

Voznyy (2022). Source: https://dujella.github.io/tors/z2z6old5.html (curve entry 75). Published independent points; exact point coordinates checked.

last edited by Natanael Wildner Fraga at 2026-09-26 20:25:03 UTC · history