curve #732

y² + xy + y = x³ − 758687094342290885696476x + 219354245751887284934326693352455598

a-invariants: [1, 0, 1, -758687094342290885696476, 219354245751887284934326693352455598]
rank (lower bound): ≥ 18
torsion subgroup: trivial
conductor (N): 552428092865891945816298025850790389506842471839193558250700550
discriminant (Δ): 7162880017550522582909570325708404392151870070852645334143225017271937500
Faltings height: 12.7042
naive height: 176.5712
primes of bad reduction: 2, 3, 5, 17, 31, 11933, 585631247017746561053058605095814470247032831728355507
regulator: 5729874520651862967.2654394821943569018656994199096573214922574331129821563
submitted by: y011d4
submitted at: 2026-09-15 01:29:08 UTC
last updated: 2026-09-15 01:29:08 UTC

(8827439505312967/1473796, 829246296424912505836284559/1789188344)
(235616244415096, -3616636775900273801158)
(341430686602, -10837285551988114)
(36002331023827, -215958274286542770439)
(816244776547, 379350970479202451)
(143645774013313/9, -1719108944573654554333/27)
(1065128796583, 787173339517213829)
(-168240291348122/289, 3345660821068832071318/4913)
(4340562954172, 8871555980094102626)
(-301791410686568/2401, 65792086192873288231229/117649)
(4290855196087/4, -6399443649805503683/8)
(5308847200944613/2704, -352861550599963148089267/140608)
(-964149835423280093/1503076, -1225246494555757979832099029/1842771176)
(1119268418532, -878838685824459854)
(1830936349627, -2228934630208922239)
(15484741666183/4, -59489156270893212887/8)
(-128612153556160599638/1330717441, -26221329437964886910583165602606/48543241530239)
(-14562601612519266482858/15250027081, -509062499356513388366420282416559/1883241094259771)

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