curve #3101

y² + xy = x³ − 87362539812439413437833065426284x + 1241608478171540522727605890546080801398358040464

a-invariants: [1, 0, 0, -87362539812439413437833065426284, 1241608478171540522727605890546080801398358040464]
rank (lower bound): ≥ 10
torsion subgroup: ℤ/4ℤ
conductor (N): 86459235830591416435905931905748037526
discriminant (Δ): -623294326045989324004161390365588274795275083594229540736171888566661062178861181340257620970500096
Faltings height: 17.6396
naive height: 235.0041
primes of bad reduction: 2, 3, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 73, 1367, 1931, 5905499, 29036999
regulator: 107945504.5767666889369837498086776401859771635955981525874
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:37:21 UTC
last updated: 2026-09-26 20:37:21 UTC

Witness: 10 independent points log in to add more points →

(12671735539611790, -1472857965505361554356272)
(-5742943676520860, -1246561784318309584428668)
(2138788584575050, 1031766535181282505457558)
(-6702171337531556, -1235342734384161373398716)
(-759249792205406, -1143460008124367165861378)
(-12995920712039624, -426652860429217686365708)
(28054933432416298, -4568601038777740126291424)
(1152874383209740, 1068841779862998610161328)
(-3563935899462440, -1227882379605974010717548)
(-12170113713276020, -708720448433330741811152)

Commentary

Eroshkin (2008). Source: https://dujella.github.io/tors/z4old9101112.html (curve entry 29). Published independent points; exact point coordinates checked.

last edited by Natanael Wildner Fraga at 2026-09-26 20:37:21 UTC · history