curve #2807

y² + xy = x³ − 178713244550246332063776938470605x + 28147864949458728271564240536379650884906835995025

a-invariants: [1, 0, 0, -178713244550246332063776938470605, 28147864949458728271564240536379650884906835995025]
rank (lower bound): ≥ 4
torsion subgroup: ℤ/9ℤ
conductor (N): 28352480766588873916770
discriminant (Δ): -341909293686297566077998559177502779659929245706014307451860138993072903043647112803442229248000000000
Faltings height: 18.1616
naive height: 241.2463
primes of bad reduction: 2, 3, 5, 7, 17, 31, 37, 41, 71, 3433, 4481, 154621
regulator: 195914.5087681290415403782302971061364423143486
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:23:18 UTC
last updated: 2026-09-26 20:23:18 UTC

(101629293809588610, 32552494216369407363685695)
(-15202948761734070, -5229816529060178755649625)
(17334183174096114397199346/271227961, 74445992775872903454362900009494808403/4466853289709)
(862411646113780429977408418/151606660689, 308518103427511192437597862833954996411673/59030630652493863)

van Beek (2015). Source: https://dujella.github.io/tors/z9.html (curve entry 3). Published independent points; exact point coordinates checked.

last edited by Natanael Wildner Fraga at 2026-09-26 20:23:19 UTC · history