curve #1975

y² + xy = x³ − 579352424306143750269326367254022350x − 57305844527587581171925109677515882551564446162252284

a-invariants: [1, 0, 0, -579352424306143750269326367254022350, -57305844527587581171925109677515882551564446162252284]
rank (lower bound): ≥ 16
torsion subgroup: ℤ/2ℤ
conductor (N): 24099481162217907061017365437216579033120419174904643226151662
discriminant (Δ): 11026717903984467415665060413805572492943057576351101410402897714149628715365750727109878815156262101103592192
Faltings height: 19.6155
naive height: 258.6553
primes of bad reduction: 2, 3, 11, 19, 23, 47, 79, 89, 197, 241, 311, 337, 821, 827, 859, 1627, 1697, 1867, 2389, 46723, 713107
regulator: 405561100730880647.7734743541813871746906315406829266264779943117812930
submitted by: dujella
submitted at: 2026-09-25 20:14:29 UTC
last updated: 2026-09-25 20:14:29 UTC

(4068219982994569252, 8057076720692148470663852794)
(-159476824589571716, -176157568737903201199725614)
(-209853749376245894, -234588510714978626702493824)
(-107903036268023300, -62862699807490056665190254)
(-407801248649888348, -333371702260952310503250566)
(1613028824672285860, 1790268242183837943924354274)
(30137928799613156340, 165398321581137978397389526626)
(-506128365115627052, -325987747254270204992027702)
(-217463635196806404, -241657382008399231119213582)
(-88925497540480809020/289, -1488795305143131800163175187782/4913)
(35980501480598807236/25, 180710978447160746595995035226/125)
(-108649531186230838766/169, -488497210480488264517264360904/2197)
(1872997724883320479900/441, 79716688493077586388902961013994/9261)
(-11948308108048013246/25, -41536210844661615551058892402/125)
(15772717897243037206, 62567722337928961199276631718)
(437004697917082731616/25, 9126719659481798690782010500346/125)

found by Dujella (2009)

last edited by dujella at 2026-09-25 20:14:29 UTC · history