curve #4135

y² + xy = x³ + x² − 299348156476240704057152x + 57978319654553649499760978999357316

a-invariants: [1, 1, 0, -299348156476240704057152, 57978319654553649499760978999357316]
c-invariants: [14368711510859553794743321, -50093268181642118504124932508905295869]
rank (lower bound): ≥ 19
torsion subgroup: trivial
conductor (N): 36091913770625384059061651858935898310189317418560618244320146230
discriminant (Δ): 264598842830897346882995735190823804486575433324822532503672072048687500
Faltings height: 12.4446
naive height: 173.7813
primes of bad reduction: 2, 3, 5, 17, 23, 319865341819936323547, 9619327548916066792686752853081977159833
regulator: 2382148111203157268.130393804615420459439587709117294593744077474913295655423
submitted by: Andrii Prokhorenkov
submitted at: 2026-10-11 01:05:31 UTC
last updated: 2026-10-11 01:05:31 UTC

(1409029733574811434778959616787/806648236774288441, -1597942423244795523131246235076741448059674224/724479803843899350985918739)
(842617512707, -635613790349340616)
(70806320232615315/17956, -18667938010286118958177329/2406104)
(1286200813669129393/154449, 1455612070209170998091643538/60698457)
(6190794152781579/12769, 236254158690952669334709/1442897)
(-64821994710479563/229441, 38071298170495239152664451/109902239)
(1292150792382797/2401, 27020272006178873154221/117649)
(-343000491790283413/2374681, 1146753669293347637111356849/3659383421)
(21409670678005888/29929, 2372166296208736973011318/5177717)
(109523340809972378/966289, 151695750477737842955250328/949862087)
(7501248787524400/17161, -231966018721600822437314/2248091)
(178988961807, -100660816440365316)
(-5436928520462/9, -3657838532803727182/27)
(63968475643981509942/142587481, -201285264969746296201258535886/1702637110621)
(584792692057, -287942244705409366)
(170448926114238662/271441, -48499050401609188715115776/141420761)
(7612286475009162608/11648569, -14951599708133185525676345102/39756565997)
(1826756221900764500833/2772759649, -55926126396745036362134964320158/146005204837393)
(146317086759934673/369664, -8714349865420128452492567/224755712)

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