Properties

Label 2.193.abv_bjn
Base Field $\F_{193}$
Dimension $2$
Ordinary Yes
$p$-rank $2$
Principally polarizable Yes
Contains a Jacobian Yes

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Invariants

Base field:  $\F_{193}$
Dimension:  $2$
L-polynomial:  $1 - 47 x + 923 x^{2} - 9071 x^{3} + 37249 x^{4}$
Frobenius angles:  $\pm0.0526881694498$, $\pm0.250841491310$
Angle rank:  $2$ (numerical)
Number field:  4.0.30262893.1
Galois group:  $D_{4}$
Jacobians:  26

This isogeny class is simple and geometrically simple.

Newton polygon

This isogeny class is ordinary.

$p$-rank:  $2$
Slopes:  $[0, 0, 1, 1]$

Point counts

This isogeny class contains the Jacobians of 26 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 29055 1374040005 51676117079535 1925144786215617525 71708910713168138108400 2671084580066587565478077805 99495242843763620887184413567695 3706098377210444230491591851302361925 138048458689188174678055166902231833930855 5142167038129222371445837886030778930081926400

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 147 36887 7188165 1387503739 267785206002 51682532469959 9974730102163281 1925122949467230931 371548729883636735175 71708904873338269761182

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{193}$
The endomorphism algebra of this simple isogeny class is 4.0.30262893.1.
All geometric endomorphisms are defined over $\F_{193}$.

Base change

This is a primitive isogeny class.

Twists

Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.193.bv_bjn$2$(not in LMFDB)