curve #1869

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y² + xy = x³ − 233446160622707474016036227307159095895x + 1632783744311672547745801285798552502904050492656782949737

a-invariants: [1, 0, 0, -233446160622707474016036227307159095895, 1632783744311672547745801285798552502904050492656782949737]
rank (lower bound): ≥ 24
torsion subgroup: trivial
conductor (N): 316824839592760145039405160672638328509656686232134875712000948213720764558320625535030
discriminant (Δ): -337487521759648549252495131685022660254841684841506377153549076723816354437024522094361931057989538796095502592000000
Faltings height: 21.0784
naive height: 276.9984
primes of bad reduction: 2, 3, 5, 7, 19, 23, 29, 67, 79, 167, 499, 269899191308721599326711801556944635559567271379228390169384519782598339
regulator: 849671582640672739205977.22222146353011551300041115464936776962081642945535009365851552
submitted by: Ritik Jain
submitted at: 2026-09-25 17:21:04 UTC
last updated: 2026-09-25 17:21:04 UTC

Witness: 24 independent points log in to add more points →

(2314100577338651694, 33240908531920744912191298533)
(3798542500362231572073202639030941103673295306304498134/124479007303970991127515494799422881, 6649655260614827098509774586303778091954566315556248922449880020977249675618433403/43918163821815459160057977047435211029664771794131471)
(151525206074222929996154/8281, 44502908849577973197279724268589323/753571)
(1206697838503186606075494/19321, -1289850562926505841150521089762500433/2685619)
(25872268092096486359526/1849, -2644019192123382150942281605119729/79507)
(7369684573360804828836/1369, -1168412555343645996149691322431231/50653)
(677955204860278499934, -17647870920039632475970219313787)
(24226283810510871414, -100975083711022460817464713707)
(-9927216006376763706, -54515418594196647037500470667)
(120235524673948093464, -1308342046694791847659165859907)
(88344999594029170914, -818857421660954969456803932207)
(63812828540787272214, -496574949904294359783034724907)
(287235817743317403231/4, -4767583841871632166507760636131/8)
(19908134613857103414, 69825305358877768465172266293)
(-14530284070401479286666/841, 550069091886547760557700413916697/24389)
(1619374648470481135536/49, -59422516060600031776134546280251/343)
(-35847337533106042318145093424531354/2266752759122329, 3993790828671581110839455800228226771993656065822399/107921066765242228924483)
(1312097974515793303782/121, 25824116912639554233363636666543/1331)
(-1943635807484526458909/324, 309553400819797516325957229140471/5832)
(12262252063757752194, 24778921457219119082111947533)
(2562008826303704325606/529, 301922037986472440424528695623731/12167)
(932019724344640119522571244716333944/98090349468176521, 507116889528243078126843710258705621702350609060163217/30721288214272339532828069)
(2752485933562511999290318908259991666/131380256410581025, 3669467953872436002669899223917747911239735544275106129/47620632309742020179848625)
(-1155197092745422482864079488/64176121, 813680819196707866102235167374880027785/514114905331)

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