curve #827

y² = x³ + x² − 4491970142384892962737176441280540549411471809270620x + 121330705843631087687716018140080411548267499233347086983266406993504041927600

a-invariants

[0, 1, 0, -4491970142384892962737176441280540549411471809270620, 121330705843631087687716018140080411548267499233347086983266406993504041927600]

rank (lower bound)

≥ 29

torsion subgroup

trivial

conductor (N)

279896977593621657628164446859079773561404867907324729157121333464884289001522205206692412030600152405856829066452167125186626520

discriminant (Δ)

-558696968003823531648916119443130386465728501718951908953256838538434960135803067135061414840456856028720363233375685797718417578956765888980694203820000000

Faltings height

28.6427

naive height

368.5079

primes of bad reduction

2, 3, 5, 7, 11, 13, 17, 19, 31, 43, 47, 61, 131, 179, 1698650475538758686544782736034780008287199049, 6770116295381328522493624034756336483124676965443153692335460151

regulator

13873641689489506918906784081615430.3135192363487313809754468583585904783818485952236530288122797

submitted by

thomas

submitted at

2026-09-22 12:09:05 UTC

later contributions

primes of bad reduction recorded · Daniel Błażewicz · 2026-09-22 15:17:14 UTC

Witness: 29 independent points log in to add more points →

(-23887653784511627008079630, -463683685644914755140836271320391751410)
(38717923769698849785646660, -73838481506265007134104170031340763500)
(14916037147909082789705110, 240097801020051219280175004990560419950)
(-61352691326724227208499250, 407411662451943904218778382949323757510)
(-77774153544039816542223305, 15751409368543049782075195614271020390)
(1443818557096072355188927294/25, -29190754530990630120098466474730914169422/125)
(32579466154419343296475810, 97802178920362035255516203520241783650)
(21801234091601987985505510, -183744944979977658996257685423161443650)
(19168769589946947060506110, 205593217284243342671396727500641639050)
(41304488446405966888834660, 79121072961271463908534632692986558500)
(30138275929401691084104535, -115436297151253766624656615745906999250)
(-1279810673369659220561090, 356479285449735099519071918186071725750)
(155712926855030573755227910, -1788118786922486360857072503339515657250)
(170199859777199340840425605/4, 680433966191382154384012124048363252655/8)
(-77713127763035598948576365, -32871171484293966812504860118843409900)
(49568505058479848145590710, 143045786028240626500378189622400232050)
(16184370798850250716308756406390/9409, 65060738522854677610286272992225192477177601650/912673)
(50533175386210800772173610, -152901272634616160207732641168192459050)
(2861441431485081714787020535, 153023895683094544733489465692339048154250)
(2757148004339804863179035338, 144731487738816781615586005907419082071734)
(-68762525125164068943128690, 324162164706069565133271270965144086650)
(157131690599116411963980303880/1849, -47260125656376332994106826119634252267923380/79507)
(55464160296412227306841710, -206906396468012309279710180613640526950)
(346604768562156419937162790/9, 1994342459393510161711177939825052714950/27)
(21115246770300605771887024056715/597529, -37871987688499732896644124292123203739363502400/461889917)
(606647071232231872085069950, -14854458966845506888941254791803325644810)
(-33539979633307991739969470, 484005326212442152603512591122949578370)
(681267687021964140042757286317540/24078649, -15354037603978333592076804516894098082156184452900/118153930643)
(56988833344996937537118660, -224550101188029857989368890947996819500)

Commentary

No commentary yet.