curve #6229

y² = x³ − 852252019551286250325151428372748x + 18870610488283477083931258439324353284770750098228

a-invariants: [0, 0, 0, -852252019551286250325151428372748, 18870610488283477083931258439324353284770750098228]
c-invariants: [40908096938461740015607268561891904, -16304207461876924200516607291576241238041928084868992]
rank (lower bound): ≥ 24
torsion subgroup: trivial
conductor (N): 17313450425430843095682349229127984689897744148618496293189985459649985243890420353640
discriminant (Δ): -114217945599678922527458607627945283888310653713358592743578984759203655599557876471186467454209401600
Faltings height: 18.0820
naive height: 240.4465
primes of bad reduction: 2, 5, 11, 13, 31, 67, 71, 113, 337, 538994594022179881867500084018808318480554179434157787791061841671057781
regulator: 1977268118884976862909648.4107067938056289883101413711532021186079526048019892348835457
submitted by: apkorte
submitted at: 2026-10-31 09:00:42 UTC
last updated: 2026-10-31 09:00:42 UTC

(-2099153951918206, 4544267693684212984168250)
(546074272699084, 4290149231008329287764490)
(15094445528481916, -3073351879448002399098566)
(-10899161946309326, -5183118072449571545844410)
(-410587826638450724/25, -666586913292646793931648274/125)
(162683307487647324, -64697579824350631154490010)
(49074250928375542, -9758669033916034609989170)
(49936993763960634, 10041899977099877071393690)
(-2885674212115658, -4615831758243487362826190)
(199582442151185734/9, -89045016443457985462555718/27)
(137677192357597161/4, -44045668214208193591274645/8)
(1930657956128268249/196, 9277574694333958203899518525/2744)
(15981625035050626, -3054855561864279977099066)
(66939428353852014, -16179288190738938833103250)
(83327912227259236508/1849, -674602012427299531438728886450/79507)
(891424292992468361/4, -835111486763905519315106245/8)
(16804909001918998, 3048668991182854776104654)
(1470695775693676, 4197664598195444232708566)
(50373996891557442, -10186524429599040719460550)
(111630048526217324, 36259972394225242338379990)
(-36822204354746708, -571062164740823974002070)
(319731292228617218, 180088592753438763615862586)
(80679201873396801, 21800534458944112074036691)
(199641176589293828, 88350124004518121127588206)

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