curve #6148

y² + xy + y = x³ − 192541634507224640110454027365631257118x + 1059210066076048093642177672700501002849536930745331949056

a-invariants: [1, 0, 1, -192541634507224640110454027365631257118, 1059210066076048093642177672700501002849536930745331949056]
c-invariants: [9241998456346782725301793313550300341641, -915157497089705552920704506897753040549952598134292254497061]
rank (lower bound): ≥ 25
torsion subgroup: trivial
conductor (N): 7218828021951200404940854601793126733524998763444653151951999875595234335566476577098714870
discriminant (Δ): -27842731216914306940007105163358220925969543605334308484687613990638552330985195491492913745639492856610703868750000
Faltings height: 20.9243
naive height: 276.1329
primes of bad reduction: 2, 3, 5, 11, 13, 19, 23, 59, 61, 71, 197, 20411, 866053, 332866001670608368769971003273808624155475169266168780690133267697
regulator: 25611914812213893649922173.62370306712095888918931709650696255591047294713378458374977679
submitted by: Ritik Jain
submitted at: 2026-10-29 13:48:13 UTC
last updated: 2026-10-29 13:48:13 UTC

Witness: 25 independent points log in to add more points →

(1227618815553886169985/256, 64265704106569389304826450513047/4096)
(5564777518296847110, -12652342660476493016500057043)
(7127610017782691512836/9025, 25830197752669986965969484691682381/857375)
(-15754603274867725735, 13498742752469950903096800357)
(133734816609177941583135/7396, -37574582829421791606946571044484233/636056)
(-13634120353310245931190/1849, 3624366440308395539899944983021164/79507)
(208572678740438979665815/324, -95232695318956790586663638365523951/5832)
(-6205280169959458065050/441, -290289348733761556270688124938948/9261)
(6593726723352311559969/4225, -7583439990990662062467065134454827/274625)
(130886471987777903385, 1489331868901904659662729971557)
(-66043952899703699389665/7396, -28914322179165170376151262274729433/636056)
(28074190524161911689810/1849, 3215968060316993432144878642776124/79507)
(24579085943103657748496490/3829849, -70251862687085609868187679722445916524/7495014493)
(3834155593982425740, -19425252652152754054390771973)
(1820012742192497945165685/5776, 2452999731704389801466415828702437707/438976)
(68728638405089322914317612865/11371449769, 13075945641121259495319978609291355654504521/1212617289016853)
(2295697820509666528602849054913722138203149735928097/293939759525604811418353699594801, 28435701807078414091595340038207835635606134829407837643439011943409900698527/5039500606563088719048393442574273415704492467799)
(9889264337078925041565/529, 768832254851469516001122216127319/12167)
(5894495588463067185, 11361292234225306153630548757)
(193639093482467689851673965/22591009, 667049992946998746857526363592001154289/107375065777)
(48804705469989480079727/7396, -5545215683860657179084496804117101/636056)
(168153403154930647812057/18496, -19512251492771497309167405532257407/2515456)
(70957840928576003905/9, -150958645066013686118667987161/27)
(-1956236291345588736615/961, -1131555202680597516507432283617413/29791)
(526782696842161247385, -12086431859502156430442592274943)

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