curve #3021

y² + xy = x³ − 244225635073705856645045305358516300x + 47380375332133580095127079115821390516194400266490000

a-invariants: [1, 0, 0, -244225635073705856645045305358516300, 47380375332133580095127079115821390516194400266490000]
rank (lower bound): ≥ 8
torsion subgroup: ℤ/5ℤ
conductor (N): 43062211048210759214042283651195210
discriminant (Δ): -37501009083084152199728978719848147286950788535323613300898798208251398589338905283062633907968330956800000
Faltings height: 19.2367
naive height: 256.1032
primes of bad reduction: 2, 3, 5, 7, 11, 17, 19, 23, 31, 47, 59, 71, 73, 265891, 21181542195061
regulator: 8695710.27884904435142081436494105715501945412030039845
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:33:40 UTC
last updated: 2026-09-26 20:33:40 UTC

(215794269656731132, 68751803745826886566570852)
(171914770006422040, 102348760844784979939372660)
(168441145048264840, 104984820306486247545709300)
(221867993820059800, 64156572929980734493827700)
(179306589562588750, 96715921232165023539184450)
(234348514776775150, 54924490017815272873228450)
(-287753405371733000, -306317759077334372898344300)
(63621460365170200, 179164459984599002204298100)

Eroshkin (2009). Source: https://dujella.github.io/tors/z5old678.html (curve entry 2). Published independent points; exact point coordinates checked.

last edited by Natanael Wildner Fraga at 2026-09-26 20:33:40 UTC · history