curve #1390

y² = x³ − 1348563007659116047368487327755608739530083261653300x + 19195671484860615809724631214458220986177210079207936667912378784395837368900

a-invariants

[0, 0, 0, -1348563007659116047368487327755608739530083261653300, 19195671484860615809724631214458220986177210079207936667912378784395837368900]

rank (lower bound)

≥ 28

torsion subgroup

trivial

conductor (N)

33521549435370896156303389464603860694689004697211578375191854446153515422170704127690619678755596784456641529115715332556600

discriminant (Δ)

-2218980537597412178389289570184582205921587334527312296198066683464718426343273562162003137042867362435719794689290592214127902537323274037338412906720000

Faltings height

28.2514

naive height

364.8203

primes of bad reduction

2, 3, 5, 7, 11, 13, 17, 19, 23, 31, 43, 47, 73, 101, 5399, 1663287404241493838771, 492173873427254772584387, 111512367159120253271849096022481569494114016031906419337

regulator

166753727494706678125989354408164.9044902325463464069206132744466371644762200680528905347438729

submitted by

Ritik Jain

submitted at

2026-09-24 21:25:05 UTC

later contributions

primes of bad reduction recorded · Daniel Błażewicz · 2026-09-25 04:52:20 UTC

Witness: 28 independent points log in to add more points →

(1155788966020678568996091730623097625843626096015929268488834646691440/61287764840282726065161971399650110469579369, 10409780890537821902139827396180661711871225322034780781809773481283511243266511348825999186034024349110/479800475943787505860329908660424401461880276131380389842105276597)
(-22383214546058495256714308271541130/1133736241, 7453696987726262716805453642890701356020576943285670/38174032970711)
(25374959130211319711540654944/1681, 3289879074555088996312994923485439801133922/68921)
(-404400648875793223104116756840/34969, 1192298889789863128939106053138813839001858590/6539203)
(-5567053633529029458892756186/169, 366799109554061255310860664585259819662638/2197)
(175021158499730364743233702105/289, -73089460888554241027118338623376809390764235/4913)
(590119759416754273105905874/25, -2837764714286819161594142712337986226818/125)
(1065980312990547057850010, -133264178068420034444085475829541694630)
(60910109089587299578041084904/2209, -5663112211723958545419143007601432893536358/103823)
(72399084093617641517429700550/3481, -2469303507839411035669514896951734024263070/205379)
(-785016197314271981141923183135/44944, -1843186970765289275833078988025390421317892015/9528128)
(88071902898619592865401401/4, -106482976193605053245188509582813379251/8)
(11810916209317448413975001584/121, -1203496588630967666098748409626002142299398/1331)
(168404652275975164107188903146/6561, -20525767778640411563452100066262526079934106/531441)
(11576556850056271993696810990, 1245566533451612156515030347697447845577530)
(17170617595129645092252676499465/1261129, -82075894904051153977226880538277407597239871085/1416247867)
(118365334968320337892216996026877803247094785/5016992490069800881, -254161509910143152781604920116229597345796447516562332771842179895/11237382828421768097812328471)
(26365135747010105396845030, 44357276536552985988887385245189459370)
(755008530311206426244012275255942273136078986/7765843565860384489, 19441428313214510252137502210651014491835677025680410250331824683166/21641280638688256203234897013)
(113806700000743937535192097272234400/6399840001, 14819942887688493540275175625888268537765341534689330/511980800239999)
(14498581542222102403838711726065967230076344/557158430122950681, 17269138253367399322362711892737281065575364142113252766602601278/415880022732393503253192579)
(3828064455646863616219931519569/182329, 911157204992574084991205394090501365316435153/77854483)
(15620600501397558581417478224878324862346400/727005527026808481, 7319498344348871188038938709101894135826649040016144803668456430/619878493455355806211145871)
(13941530399448343320992277453400/727609, 12268855376323075686085372203031268468522446590/620650477)
(2674004849654405138052710162561482586438553491524876471524004107699366985/125028282369253828220797554713944820453998990096, 516422142333215052143740883196654477412603476025190810331048196012717818307361913977549090347862725722846405/44209173663856803975638544425135349753495678443383247108867649048081856)
(-6855788625809810827072585539095/201601, 14519338480410520101176249901938663158999579245/90518849)
(-163087168103201384362710373775/6724, 106965310399708258477245877726769172241537815/551368)
(86452616571150613570292893267593936571879465/1912797633426447076, 594916788263087304456994146156859586146527085411833567831244548405/2645474250243031496390462824)

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