curve #4136

y² + xy + y = x³ − x² − 10958526220066814718603894x + 13852523739455061367026324921569414277

a-invariants: [1, -1, 1, -10958526220066814718603894, 13852523739455061367026324921569414277]
c-invariants: [526009258563207106492986897, -11968580510886805979447210300256755494521]
rank (lower bound): ≥ 19
torsion subgroup: trivial
conductor (N): 7360643757325984425726315118033201479661698976183861659409428914
discriminant (Δ): 1326586548837216802392682260472776938329657300359358965750086055777859846144
Faltings height: 13.2369
naive height: 184.5821
primes of bad reduction: 2, 7, 11, 17, 12792174664533995376586039837, 219786886206569068183918264243729
regulator: 1387458930390551656.036238058163384043312057614455773977164156678309320493759
submitted by: Andrii Prokhorenkov
submitted at: 2026-10-11 01:06:30 UTC
last updated: 2026-10-11 01:06:30 UTC

(79243221627286210636585752295/71642206963463161, 33678425847129480460658904762441002580836209/19175797462366660056956659)
(269494561385, -3304365911977018837)
(1852989813619105/6889, 1889873255392552856540937/571787)
(13061556680361877485/6370576, 903304197738991289944009037/16079333824)
(-142095454668179271/61009, 77926108821929041402993421/15069223)
(17775382116322573981/8579041, 5140305020314005613798756159/25128011089)
(205198834601713/64, -1749570244007529708147/512)
(6546756572642699921/4380649, -8267799789291146685253573081/9168698357)
(173605679766470833/59049, -38091035556076514853381767/14348907)
(18430533472996594229/11015761, -16401625659349631474019540907/36561310759)
(-83919625737326239/22201, -3721726803798473033228977/3307949)
(-118715482708039/121, -6474151890375081348839/1331)
(117552601153225/81, -730966664515168093933/729)
(637263535606537/361, 638185098645613103617/6859)
(32268949561401049/18225, -39014067456514801608227/2460375)
(1425692749201, 1061552481310777627)
(-122783583623153902183/37466641, 875372996174051598753063491059/229333309561)
(967522559465530041/1585081, 5425338306599121339387115833/1995616979)
(-14111162053334031/3721, 211873827473899807773687/226981)

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