curve #2771

y² + xy = x³ − 6235503349706099317232119038151880529845x + 189419104701643513972219165960187230267385337379886707205025

a-invariants: [1, 0, 0, -6235503349706099317232119038151880529845, 189419104701643513972219165960187230267385337379886707205025]
rank (lower bound): ≥ 4
torsion subgroup: ℤ/10ℤ
conductor (N): 244375491477491983033103910
discriminant (Δ): 16541109642641752806453374478365858326764730209628282609309515897497925789682759620037101127777262979248184690000000000
Faltings height: 21.6265
naive height: 286.5068
primes of bad reduction: 2, 3, 5, 7, 11, 17, 19, 31, 37, 41, 79, 139, 101119, 6272219
regulator: 473614.1819781330615558096617411825239228104884
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:21:42 UTC
last updated: 2026-09-26 20:21:42 UTC

(17589807360712156090, 291856320210123832159665884455)
(32254945713754125363142410/169, 183186909473224164721735686310561219635/2197)
(3568054094929294949476685410/859329, 213092992005335904580831819367952379418665/796597983)
(103201476065683018372809559484742207512444260180660/698317240262928282290790194449, 921872016140031983045959981157221175214685946760439597841749424753905185935/583551441562923065277439175513892774989278457)

Fisher (2016). Source: https://dujella.github.io/tors/z10.html (curve entry 9). Published independent points; exact point coordinates checked.

last edited by Natanael Wildner Fraga at 2026-09-26 20:21:42 UTC · history