curve #6356

y² + xy + y = x³ − 26710520884484639394125879310304132583x + 53131935624931316622009478583044991433993748879816482806

a-invariants: [1, 0, 1, -26710520884484639394125879310304132583, 53131935624931316622009478583044991433993748879816482806]
c-invariants: [1282105002455262690918042206894598363961, -45905992379940657563339346999433766635347662342503338690541]
rank (lower bound): ≥ 25
torsion subgroup: trivial
conductor (N): 33732855986999993619544451405606703356972421971246797762185023380682002670236005522920130
discriminant (Δ): 89928347205153839709000681723966814170684456308428218201706446186840909195241370807046730927052212216619062500
Faltings height: 20.1777
naive height: 270.1480
primes of bad reduction: 2, 3, 5, 7, 13, 19, 23, 37, 79, 1021, 13086907313, 175460577301, 589440333963054338458823697116472648947221618166381021
regulator: 53748066800416100490969663.83445557691598699951072594592487736380454253900803832065999530
submitted by: apkorte
submitted at: 2026-11-01 10:58:54 UTC
last updated: 2026-11-01 10:58:54 UTC

(5957118701617335795, 10267230955845700755919705342)
(3566846356846621560, -1799564505579380811277943078)
(2884932791328360315, -291039581614883829068136158)
(11995446397992160455/4, -59378355790734728560050139/8)
(3012337784560490565, 72913432503974841994601842)
(3140898858214141497, 471836660285503638537404728)
(3913011511505206380, -2920283926820160524411093123)
(6334378053554446425, 11751602899305100760248621432)
(3929346701455413755, -2974093163406167843784775758)
(1786782800471195160, 3333242591250112091493627322)
(18657955415909731960/9, -69720263390621237809692360641/27)
(27537902443666033210/9, -6039588433561363045475960641/27)
(2999639013044224275, -16420904335147503964555418)
(12547822962185626635/4, -3678256413581532458649167389/8)
(2629278651424047165, -1038756908478992429025876758)
(2999446339025801025, 14678448106471984467501142)
(2955282688117214715, -73044967000605958218018158)
(118476097639801128315, 1288366591014282688358685803842)
(-2194494198786605355, -10058815191639500922063200408)
(-5893982658784452690, -2410815792091014244678388828)
(-3508633644913680195, -10181173708143688214590020758)
(2946645052129972190, 101964179968126370570767092)
(646765124361714409815/196, -2636463718436314532913439814677/2744)
(1899438932056839030, 3041357884891259914352509852)
(145082744073422535195, -1746432065035489638732183570038)

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