Properties

Label 2.193.abv_bjl
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:  $1 - 47 x + 921 x^{2} - 9071 x^{3} + 37249 x^{4}$
Frobenius angles:  $\pm0.0309899411438$, $\pm0.254827200630$
Angle rank:  $2$ (numerical)
Number field:  4.0.13811661.1
Galois group:  $D_{4}$
Jacobians:  12

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 12 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 29053 1373887317 51674087446189 1925130499891213989 71708840483714602651648 2671084310223994760780534421 99495241978953975588177218857021 3706098374750481312206061287872611525 138048458682408631431722239149415792242061 5142167038109172629618696537913117995536023552

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 147 36883 7187883 1387493443 267784943742 51682527248803 9974730015463227 1925122948189409731 371548729865390021619 71708904873058670709118

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{193}$
The endomorphism algebra of this simple isogeny class is 4.0.13811661.1.
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_bjl$2$(not in LMFDB)