curve #2102

y² + xy = x³ + 3311205881636709019224401409915301563913740x + 3216335426815736716552028523390682092286549833602271251186259600

a-invariants: [1, 0, 0, 3311205881636709019224401409915301563913740, 3216335426815736716552028523390682092286549833602271251186259600]
rank (lower bound): ≥ 9
torsion subgroup: ℤ/4ℤ
conductor (N): 66383858512923544794969205407447187710
discriminant (Δ): -6792437271740821541072548895071010205743664298321278974607880076889209389356859575124755200059267680885130719069790590745405440000
Faltings height: 23.5974
naive height: 305.9854
primes of bad reduction: 2, 3, 5, 7, 11, 13, 17, 19, 23, 31, 41, 43, 53, 61, 71, 89, 101, 127, 193, 421, 1289, 198377
regulator: 4704590323870.7268399320014857134606247084399637018990196
submitted by: Steps Unbounded
submitted at: 2026-09-26 06:57:10 UTC
last updated: 2026-09-26 06:57:10 UTC

(203398285796966916414471720/57121, 3348385798477885898206725724142321249460/13651919)
(-48456654494142775111848600/63001, 231621882641877283822986824662386647460/15813251)
(-484077600102156287509324392/896809, 30286623082862303865615687454568403214836/849278123)
(213794812657778109436292639770/222218649, 282885420581324371256544512782877927593396840/3312613400643)
(5389980024313956753303881882826/95433361, 12520160485248413715586010828816706513028862958/932288503609)
(40373930468859067225194170640/4739329, 8316059303022720457595218844028561041098020/10317519233)
(2333984323128418035515433361798779863784/14071730481705625, 112764705359316586078117095160469385018900312576469529585052/1669249529974254614328125)
(-5003635763082558601354215996113702/6377175444249, -187310489399785583322684988801365730317225386492824/16104325789590109443)
(-729295965074341450465951993585912320/4842735949473361, -17557488836291419459078932710621548577493526291413637740/337004876051846863643609)

2-isogenous partner of curve#1828 (Dujella - Peral (2019)). Isogenous to curve#2097 (also ours).

last edited by Steps Unbounded at 2026-09-26 21:46:16 UTC · history