curve #2777

y² + xy = x³ − 19194775548787283845230607299614214311678x + 1023582059693167156639765281299410390763594972426927678761572

a-invariants: [1, 0, 0, -19194775548787283845230607299614214311678, 1023582059693167156639765281299410390763594972426927678761572]
rank (lower bound): ≥ 4
torsion subgroup: ℤ/10ℤ
conductor (N): 270662653535270356603978350
discriminant (Δ): 11181401929509633936947765095679652758547639621025404231848103157095092405298809752569733206526305698204222883276000
Faltings height: 21.6289
naive height: 289.8800
primes of bad reduction: 2, 3, 5, 7, 11, 19, 29, 31, 47, 61, 71, 157, 241, 307, 580219
regulator: 1593418.583743987440421618622392313023464379589
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:21:56 UTC
last updated: 2026-09-26 20:21:56 UTC

(-72916487552680553369672/529, -12470497160653492460311828196091562/12167)
(3800850833657108380680857998/413449, 234299952032482293627366132672200635358548/265847707)
(1038663796752458552287654/9025, 499085422584595640129514287454205868/857375)
(9299986225503696073397435648430959777336325444966169329232/118582088494247866469775586700363663089, 31154049781500818599931128211014876857065379953409468100300331357090737532995533586570/1291304434505042263235924994206689677621210701220944773687)

Fisher (2016). Source: https://dujella.github.io/tors/z10.html (curve entry 8). Published independent points; exact point coordinates checked.

last edited by Natanael Wildner Fraga at 2026-09-26 20:21:56 UTC · history