curve #3921

y² + xy = x³ − 580936412399346098776991752378440x + 5298919075560531097792268337873423005739128001600

a-invariants: [1, 0, 0, -580936412399346098776991752378440, 5298919075560531097792268337873423005739128001600]
rank (lower bound): ≥ 11
torsion subgroup: ℤ/3ℤ
conductor (N): 13922574053879389445811261009084209696418489630
discriminant (Δ): 417816718216082611239796593939891372673334747888309222268330640714726216204309645890448339392000000
Faltings height: 17.7165
naive height: 237.9402
primes of bad reduction: 2, 3, 5, 7, 11, 13, 19, 23, 31, 37, 41, 61, 127, 199, 277, 157747, 25761113458230472969
regulator: 30977535408213.6971547347986431617155799348387164268312371391
submitted by: Maksym Voznyy
submitted at: 2026-10-04 22:41:10 UTC
last updated: 2026-10-04 22:41:10 UTC

(3925519277873523717444935065230/247582326093001, 1058938124303065354305507672185345760028738740/3895645757909521391749)
(153283850815938347064/9409, 363357592306457519162273815416/912673)
(102775710625886446584240/6205081, 7261161021659410934186036232640200/15456856771)
(703322553228990012266767578480/8627666669521, 566477423894554665908386889494938599810284440/25341950404050668569)
(5943614709014861480446620/130804969, -12757291988822504920622593684087053720/1496016430453)
(2448138130119987692794819409358243372/120954938054192468521, 1800663510064556822995943149838236672457924695442028324/1330256547122755724572741003819)
(1655990343442047357559920/76335169, -1136865119478926939143656332993259720/666940371553)
(12199800476324178279352990410517488/720015646224545449, 345656590982262581993161255494728905127485322259096/610960173446022823820838293)
(344552386392950362803120/21631801, 29628633971518982285174117356389960/100609506451)
(260073278793173175071437920/2654619529, -4077412002943337202064261382658520627080/136773961992667)
(7291406482504544429363528654880/463693301864521, -2277883341022039920738884173252584319809698760/9984957799738435669819)

Eroshkin - Voznyy (2026)

last edited by Maksym Voznyy at 2026-10-04 22:41:10 UTC · history