curve #2000

y² + xy = x³ − 70108235372134622622252283845024231998385x + 10033288229518010129524793388527045899713495537483533386965225

a-invariants: [1, 0, 0, -70108235372134622622252283845024231998385, 10033288229518010129524793388527045899713495537483533386965225]
rank (lower bound): ≥ 17
torsion subgroup: ℤ/2ℤ
conductor (N): 483715857041459117037004194204697257455321027821861096646780904570
discriminant (Δ): -21434103637471185306666292748760351521652327190607852832503198221628082532158520159639848510340062282966873903116255232000000
Faltings height: 22.5601
naive height: 294.4452
primes of bad reduction: 2, 3, 5, 7, 11, 23, 31, 37, 41, 223, 241, 307, 311, 337, 379, 433, 743, 1873, 2801, 3617, 8179, 14879, 407599
regulator: 15263643071469397745493.3199358112654652811621913326804280893758716284265
submitted by: Steps Unbounded
submitted at: 2026-09-26 04:57:02 UTC
last updated: 2026-09-26 04:57:02 UTC

(91785538315856668170, 2090842217544144838015256520315)
(3183159756888605999370, 178997913480553215847129834536315)
(128084992055605070490, 1776177852195725993298932237595)
(-119279997643934597298, -4086406273102506487855041478593)
(113683618159858002990, 1879460953539334847504033316915)
(-211980788142572328630, 3920376175603838914480488048315)
(44085339703608442541850/361, 12446544554845481587191874284579465/6859)
(18016643661089419737705/64, 1817866740025636620918265884351705/512)
(517110182184630331470, 10585669045771915079610380403315)
(-1765334793614341423830/49, -1213286201663541184729921219334835/343)
(92697846079427914961550/289, 22269451845855990468186384652733955/4913)
(-46618017184283442698310/5329, -1269288291461346826744080121874695725/389017)
(-5940437995046588323598790/76729, -82308107805206415632719183058027936865/21253933)
(28505527394861729235476730/32761, 146186383577669975959710978153038832255/5929741)
(48981684862802085587418/169, 8238134534038518678697590013056279/2197)
(-223511350504776939694216770/2036329, 11769958696347885369541057159297612158645/2905841483)
(63459957037406685899149470/373321, 396897946335935641064047788911440336065/228099131)

2-isogenous partner of curve#1101 (Dujella (2009)).

last edited by Steps Unbounded at 2026-09-26 21:36:09 UTC · history