curve #3081

y² = x³ + 19988905798337416857887750048967131889

a-invariants: [0, 0, 0, 0, 19988905798337416857887750048967131889]
rank (lower bound): ≥ 9
torsion subgroup: ℤ/3ℤ
conductor (N): 239866869580049002294653000587605582668
discriminant (Δ): -172608345366396712291323919343491753752300321995049871551086186347799345994672
Faltings height: 13.4993
naive height: 185.2996
primes of bad reduction: 2, 3, 7, 13, 19, 29, 37, 43, 67, 193, 271, 1777
regulator: 325017567507.34368434898927436093461168725960569009062506
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:36:22 UTC
last updated: 2026-09-26 20:36:22 UTC

Witness: 9 independent points log in to add more points →

(-2640021124104, 1260444411760220505)
(-1493609987870, 4081281036143667083)
(495076126904128/81, 11487657144818347102351/729)
(-5029068819772305/10609, 4872433274311350166204716/1092727)
(133138704688704/25, 1634726880503373945483/125)
(569664793333145419/112225, 461648166803843299551365822/37595375)
(6128715173559771793/391876, 15211985511221581947227379289/245314376)
(-1212444784307181698/514089, 966187173700541562163401007/368601813)
(338768307272049511667230/2363612689, 197176718832242653058548030024322629/114911758101113)

Commentary

Voznyy (2023). Source: https://dujella.github.io/tors/z3old891011121314.html (curve entry 58). Published independent points; exact point coordinates checked.

last edited by Natanael Wildner Fraga at 2026-09-26 20:36:22 UTC · history