curve #2835

y² + xy = x³ − 13595883660149605052308511455995x + 18036730221659744241723788396566551765213731025

a-invariants: [1, 0, 0, -13595883660149605052308511455995, 18036730221659744241723788396566551765213731025]
rank (lower bound): ≥ 5
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 5001003101018493593310
discriminant (Δ): 20303236239956068020126014729646466464992708754510551983230167579715621971415090496265625000000
Faltings height: 16.8422
naive height: 226.6756
primes of bad reduction: 2, 3, 5, 11, 13, 17, 19, 23, 29, 43, 107, 197, 1033, 5779
regulator: 91220.0931256662934952840757062134762621795582970
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:24:33 UTC
last updated: 2026-09-26 20:24:33 UTC

Witness: 5 independent points log in to add more points →

(117195404063982, 128237922544546185572937)
(-1056942542075440, -176708964835875437379415)
(-436816652758110, -154571310694155898077195)
(359287798699885640, 215348036226614053698285305)
(-438134746958610, -154626821586630691024695)

Commentary

Dujella - Peral (2021). Source: https://dujella.github.io/tors/z2z6old5.html (curve entry 47). Published independent points; exact point coordinates checked.

last edited by Natanael Wildner Fraga at 2026-09-26 20:24:34 UTC · history