curve #2850

y² + xy = x³ − 239247306678234007210828097520x + 45246626407933026379552521501618249969926400

a-invariants: [1, 0, 0, -239247306678234007210828097520, 45246626407933026379552521501618249969926400]
rank (lower bound): ≥ 5
torsion subgroup: ℤ/7ℤ
conductor (N): 36234340651501462470
discriminant (Δ): -7977217740530782168811753192612927591247152432589415308725010668402717491200000000000000
Faltings height: 15.7120
naive height: 214.5645
primes of bad reduction: 2, 3, 5, 7, 11, 13, 19, 89, 713545091839
regulator: 34781.4904553574930476442132241342568795714181909
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:25:15 UTC
last updated: 2026-09-26 20:25:15 UTC

(46074969993440, 5858423537724469003280)
(275652423665370, 492718372260784145100)
(138768613071840, 3836513831575606436880)
(297508887793440, 633557750590112003280)
(169967679183690, 3080992491904517095530)

Elkies (2006). Source: https://dujella.github.io/tors/z7old5.html (curve entry 5). Published independent points; exact point coordinates checked.

last edited by Natanael Wildner Fraga at 2026-09-26 20:25:15 UTC · history