curve #1970

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y² + xy + y = x³ − x² − 13577439753525837495290899830x + 610437010617328312066231002641417386475397

a-invariants

[1, -1, 1, -13577439753525837495290899830, 610437010617328312066231002641417386475397]

rank (lower bound)

≥ 21

torsion subgroup

trivial

conductor (N)

419484259838469469163780220907315175177918768124089206166785993088450

discriminant (Δ)

-788258996633307558248195148205597217510316770264196137435501803667063440197509120000

Faltings height

14.9700

naive height

205.9531

primes of bad reduction

2, 5, 19, 31, 41, 43, 47, 5449, 60577759783, 520775067178100695502122003496978431185308383

regulator

43589327957215753491.659975385041623599086256866337879245594383050841152117113465

submitted by

Ritik Jain

submitted at

2026-09-25 20:07:14 UTC

later contributions

primes of bad reduction recorded · Daniel Błażewicz · 2026-09-25 20:08:50 UTC

Witness: 21 independent points log in to add more points →

(-6093930881533150538191/45373696, -32588741867717359251461009054705/305637216256)
(331690720374947341/529, -187942262917911890351089435/12167)
(5366077171987819942574334326798340891841/89349744068885050165014889, -91092842481177161922566053102310466229706234617088773944775/844578398240147291547892210297961525963)
(-1894988092319199251/15376, 1223565318863712644692891485/1906624)
(1025569881603740169/25921, -1534373919813269345640212405/4173281)
(220102451977255166497/3143529, 307102148154648881512018462007/5573476917)
(51520760545513, 218341716295026048171)
(-13551243876681, 889909951019306971355)
(201892515216641105/3721, 41535647395793359158992311/226981)
(-38332479596229989/289, 1370623789263478963751505/4913)
(66762898405999, -39357610718700431765)
(-22488610611431899/169, -542105357585831222326885/2197)
(1168000215491069/16, -5831010361340483971685/64)
(12874460423312411/169, 296480975878035965154685/2197)
(11812610213596949/121, -617685044767550743998295/1331)
(86552045950377161/1024, -8461432221632516926131605/32768)
(26330114462686812352458809/342879342481, -28843527534731313642437789896102038995/200776084903831879)
(-427679315673176336921347/11709620521, 1303100249811956474576791765180876801/1267109746197931)
(33242346289621429988723827511/540428123352100, 1124267297688882837826708323175640733708161/12563392030659837431000)
(7798194660583447055647/124055044, 100984640386994532716633983520687/1381725080072)
(22001501392434252488097646860142729/346604321036428384801, 425652234756255563621021350282361889949022925459195/6452840924271683341104057217201)

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