curve #3880

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y² + xy = x³ − 1311421576771945493584647201719997644041x + 18282241809969491356798928648604168863954827482719223469721

a-invariants: [1, 0, 0, -1311421576771945493584647201719997644041, 18282241809969491356798928648604168863954827482719223469721]
rank (lower bound): ≥ 25
torsion subgroup: trivial
conductor (N): 311422174197808315651863568251044083375827831259526881939368912918421832448972903721231135890
discriminant (Δ): -45108426210882324866549918430079423275396144240542425682177951283445558860135063658858262850535824653659387307212800
Faltings height: 21.1956
naive height: 281.8297
primes of bad reduction: 2, 3, 5, 13, 17, 53, 59, 61, 79, 13063433689, 172046092399568533426408951769, 1386912422776149257535494585274576904787191
regulator: 56182772073852713843708469.02667405595582370716179872870546358438374669427619048099529214
submitted by: 7fff-zip
submitted at: 2026-10-04 13:58:28 UTC
last updated: 2026-10-04 13:58:28 UTC

Witness: 25 independent points log in to add more points →

(25015557200902816616, 33622734099670772039087330957)
(21434192942581196126, 4513845822497799095939191367)
(172720593898507653117866/7225, 14962316824581397575082424815661159/614125)
(46112379180038598439850/361, 9540983162174067027430678342457249/6859)
(-23171503141486002214, 190338227770322021976480450947)
(-5655858158180486387006/529, 2145027946914990240818111194818149/12167)
(21191385986397581066, 2814117514265698831409051507)
(18585531671606101898, -18128040419103035751473702413)
(34132593231770448526106/841, -4356703516123485375505504568522177/24389)
(2658150238007646595790/121, 11493030874216722131307320040901/1331)
(20017977433718382854, 7199069208775139698544400143)
(31955170933243080761162/2209, 5020693991964704795025098913938221/103823)
(4517848915708658045847050/249001, -2667596807815315768074975737399385439/124251499)
(2529932268754614457706/121, -2249334924379425352467790369223/1331)
(1575993277758609478346/49, -33209964585134517526051202842171/343)
(-706109835910290339326/81, -124255418958311160300111344896453/729)
(1314661095982445553807563546/65918161, -4154431308515902254022906214728651173547/535189549159)
(17137737226278825466, -28997099369881210705831436573)
(14228029408575952879370/361, -1143996885101120614149701734059199/6859)
(119309221896436464979166/1681, 36647518064780769875783264276673007/68921)
(3305482389616302141134/121, -70975505082604060011523286804027/1331)
(11021541711360373706186/625, -395250628365970238793037490719141/15625)
(20628424096031918276, -2780909357745144082616932333)
(19302246748803613658, 12665974492197366413254581635)
(21839024760436304336, 7618632681754969013614661717)

Commentary

X1008, t=-196/241.

last edited by 7fff-zip at 2026-10-04 13:58:28 UTC · history