curve #1828

y² + xy = x³ − 1443705842368492991301675445569878391286260x + 518524534126954116322153225511662398609137586525877978241619600

a-invariants: [1, 0, 0, -1443705842368492991301675445569878391286260, 518524534126954116322153225511662398609137586525877978241619600]
rank (lower bound): ≥ 9
torsion subgroup: ℤ/2ℤ × ℤ/4ℤ
conductor (N): 66383858512923544794969205407447187710
discriminant (Δ): 76431344543834120606650346253846757796883746823648438467421987419590458312487083792581110777083762553529114817663703449600000000
Faltings height: 23.2509
naive height: 302.8410
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: 9188652976.3100133592421904017841027826336718041052715229
submitted by: dujella
submitted at: 2026-09-25 15:37:08 UTC
last updated: 2026-09-25 15:37:08 UTC

(128223174003353679720, 18317099368470117761199421172940)
(956390935331148119400, 3545768914293555321550146272460)
(1016377111024059996120, 10055611157530821697614783806940)
(1697827353996567683370, 54420111049349435946331048024440)
(56495946288484604961066, 13425433378463019292263609689408862)
(289704950331957158160, 11162008755000776928955192667940)
(103668184309638014012632296/625, 1055496671159222837902206275138714086956/15625)
(-11988121387712302153670/9, -238796691154542884537206928300120/27)
(-26537457561058268238635520/29929, -171844066225434189468646360371177721020/5177717)

found by Dujella - Peral (2019)

last edited by dujella at 2026-09-25 15:37:08 UTC · history