curve #305

← home · all curves · JSON ↓

y² = x³ − 1268312930510319255122480259

a-invariants: [0, 0, 0, 0, -1268312930510319255122480259]
rank (lower bound): ≥ 15
torsion subgroup: trivial
conductor (N): 238313731807359099208895797698912716157803778347364012
naive height: 138.3381
Faltings height: 9.5858
discriminant (Δ): -694922841950259133293140146090029480316155817660913458992
primes of bad reduction: 2, 3, 1201, 6539317, 32344001, 61641367
regulator: 86153414289554100483771.712495893112702321066389841276794286886565627
submitted by: 7fff-zip
submitted at: 2026-08-24 00:21:56 UTC
last updated: 2026-08-24 00:21:56 UTC

Witness: 15 independent points

(47588326838434616590010425/4549729674435856, -328102728610125435524420170882337148691/306886928285470237181504)
(48747134492040886698624619/9226793750552401, -338881570401054220468807753719969542560/886290755088605291488601)
(49823244917084492275579123/12659318510967769, -348002749052775350177937935624315537444/1424345967610408079965853)
(199301527300475269347473851/50662594126759729, -2784160523202581922547251680529933141620/11403315373020564884884183)
(205241122854531989422967851/67001006847907729, -2874731558708319632458960350374575165520/17342910927077284960378183)
(55472803613702032582316083/26234111479653529, -384451829905570782692328584564863778756/4249125315919178233334333)
(62612405455637545723136713/39394120653348484, -409781851000372134548987285229467439781/7818926236886934803744648)
(307931269151900722655967595/243332757931016209, -3305266414750462671678180179609759012392/120033057224446018193377927)
(424931833887797483795805487/383006932772540521, -2338505959647951213349030577638127672698/237033621960342779333215819)
(175251870454542381865445305/160231014526904896, 406207274087726206443049260244863078701/64138658736339352874898944)
(191416404564934698417010825/173423801105283556, 631029014963680256374282820560167314491/72220925791535511150681704)
(229590696369684566507139319/202771126591924801, 1236133565139301808969423387171061396170/91308071693910445195745951)
(1867878837168554962644925369/939373017476555776, 73929979431920166196980624100828219877165/910452142093345643264638976)
(166541923543969359929742064861968342382291566388172262237913548599153229661764587719/152670168037897651998122773018557318122887950612221610242309530810377239025, 10295460717704462200089862214180338908522917498845172916896819226389517343275472239794834678280510027754503229631468510976922/1886389087416185299933674625089233661079101370516812467457349725842982018698316827142215163049646701774561367625)
(407182447583169362326223263741856685372509391899975002573221965260297404699259/286075304729757933362882514772138860508569363300257200574962513730625, 194463186392174551922926082806428734525587443038534423475320668472443928072942409784111121272476103238664769814915848/4838609277778199762289867828434248807931011106936376797095088672190481132203583935153318443859098390625)

Commentary

No commentary yet.