curve #2828

y² + xy = x³ − 10039161702346614399135276217950x − 4223829117956048597247231503907952922420797500

a-invariants: [1, 0, 0, -10039161702346614399135276217950, -4223829117956048597247231503907952922420797500]
rank (lower bound): ≥ 5
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 5150226525423583551090
discriminant (Δ): 57047656711192701774569339563074941617194795018861400918196053270309502917109849941868544000000
Faltings height: 16.8744
naive height: 225.7657
primes of bad reduction: 2, 3, 5, 11, 13, 17, 29, 37, 71, 139, 149, 1709, 26189
regulator: 330558.565277130323515061500952737084469659553652
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:24:14 UTC
last updated: 2026-09-26 20:24:14 UTC

(-887289613918308, -63128969839458539253294)
(-889512557334180, -63263890971432403925550)
(-1051463310520080, -71899300115766380321550)
(5813726483439120, 365939593694818919586930)
(4620550503364133820/1369, 934617700015308231705683850/50653)

Voznyy (2025). Source: https://dujella.github.io/tors/z2z6old5.html (curve entry 78). Published independent points; exact point coordinates checked.

last edited by Natanael Wildner Fraga at 2026-09-26 20:24:14 UTC · history