curve #295

y² + xy + y = x³ − 17376238614102880805191699606601x + 27567969093931513230545328071325120978929115848

a-invariants: [1, 0, 1, -17376238614102880805191699606601, 27567969093931513230545328071325120978929115848]
rank (lower bound): ≥ 19
torsion subgroup: trivial
conductor (N): 3776371284397311148628418800115360198487121104793824664716985153998003950
naive height: 227.4116
Faltings height: 16.8210
discriminant (Δ): 7457232482908894871013009794413777903272851601541491513138882261811971201715408443836746312500
primes of bad reduction: 2, 3, 5, 11, 13, 19, 23, 402870950419240226446306273449015079343385031955942953355094883423
regulator: 14105020090504354211.99517017105242643598673749080930699020301462209879390741
submitted by: 7fff-zip
submitted at: 2026-08-23 15:36:54 UTC
last updated: 2026-08-23 15:36:54 UTC

(4369543904550327, 187267339530688676110336)
(1195243802289372695020017/1661521, 1306704765542469239062915773397753184/2141700569)
(12967129481142123693/2809, 31835836356868164437299009772/148877)
(88874188420206963875802/2307361, 26345787016768635714902369850755089/3504881359)
(-741077948932542204/361, 1602536954426301130134942028/6859)
(653761404612892650534918/333172009, 194892641567963226211520853614424322/6081388680277)
(-113793377263026972/1849, -13454577875578070833126523243/79507)
(-7849955396966609324523/1940449, 480935126897873310433991902795324/2703045457)
(366797731113564287/121, -69800811934580663772836544/1331)
(12972338401811965187667/4919524, 99767515053863147789423836902259/10911504232)
(4967677269796568148/1849, 1322582671515705120624875452/79507)
(13791002656531647, 1552696745412643882922476)
(4372988870978271734064/93025, -288078878554022579824856072101672/28372625)
(2453524111554347023675053/70845889, -3816477238820011972315977707620789132/596309847713)
(9874999792687725596638338/42799748161, -1359414244218777757508353645152301376033/8854454699295841)
(5640126141438553812957/2835856, 141353621473124970112550664024379/4775581504)
(360824300188172676963981796533/1465850182729, -216711414718087227728440158697738320773271638/1774738530784203067)
(671374043049102, -127297410929274089424689)
(1500720948727546002333/966289, -62484986760065438493669881108788/949862087)

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