curve #6150

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y² = x³ + x² − 43860811484397345811817032445974580x + 3846189722890651791198162728952089915028190122177600

a-invariants

[0, 1, 0, -43860811484397345811817032445974580, 3846189722890651791198162728952089915028190122177600]

c-invariants

[2105318951251072598967217557406779856, -3323107920577523160227126305321041280387661610002125504]

rank (lower bound)

≥ 24

torsion subgroup

trivial

conductor (N)

846891273458957535533514951019200697928811397787093226654378971382431761784216994895560

discriminant (Δ)

-990450313337065490121283900372453674149748578704576892265880356413537030086431819100678634244392700000000

Faltings height

18.8855

naive height

251.0810

primes of bad reduction

2, 3, 5, 7, 11, 13, 89, 3868517, 409338772943, 73952597487411674503, 676459035407216902407707558643327567745619

regulator

3432759773313922264741756.7399851522647278850907900761119234488944298533818896350660563

submitted by

Ritik Jain

submitted at

2026-10-29 13:48:21 UTC

later contributions

primes of bad reduction recorded · Daniel Błażewicz · 2026-10-29 13:56:11 UTC

Witness: 24 independent points log in to add more points →

(24895155057631940659753582475072661232732935490/155346143698630893103095740041, -1870139362507288064882749820250686725510305187115742025718612048729250/61228090471132084006948575437753844563239589)
(129437402024402190, -18372799995152947371038550)
(6295434996284631010/49, 6247652390529448757345187450/343)
(16400300625534040020/49, -56005128619923505696955736720/343)
(-244005346660796177, 4552280378853631046871066)
(-769171097974235030/9, 2254210735527098777304114470/27)
(-202813381084080860, -66327762897138007365555000)
(1319541576610115950/9, 643020651309194743158269630/27)
(-133179478208332160, 85588407401675855785291800)
(82446496482645540, -28114824230611710550865400)
(-219921920389106210, -53436661111083133543446150)
(-326026360322780360765/2809, 12783822004668041757945661255200/148877)
(111318278247071140, 18523201404286342877607000)
(8227929611442225250/81, -15273713656990543370885058790/729)
(361633613847846820, 187826200443089767761103320)
(178363038948240336625/1024, -1265298355322612587860208640055/32768)
(17675649234222918217/144, 30513522080372936895037045837/1728)
(9340423852013059525/4, -28435589197588998136981764495/8)
(1227150601682836948, -1340890279110890260420565184)
(247324351736114560, -90149925520885523692624680)
(5450603813517252668410/5329, 394620561299725130411824573968450/389017)
(-119568186995455985, -85913530413161445678863250)
(14301807252888080590/121, -23557147007411687211296197650/1331)
(38579751640182258217/64, -226934459854897771173477805707/512)

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