Properties

Label 2.113.abk_uu
Base field $\F_{113}$
Dimension $2$
$p$-rank $2$
Ordinary Yes
Supersingular No
Simple Yes
Geometrically simple Yes
Primitive Yes
Principally polarizable Yes
Contains a Jacobian Yes

Learn more about

Invariants

Base field:  $\F_{113}$
Dimension:  $2$
L-polynomial:  $1 - 36 x + 540 x^{2} - 4068 x^{3} + 12769 x^{4}$
Frobenius angles:  $\pm0.0305767614990$, $\pm0.254114540183$
Angle rank:  $2$ (numerical)
Number field:  4.0.1542400.2
Galois group:  $D_{4}$
Jacobians:  4

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 4 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 9206 160313284 2081171411894 26584739701910416 339455604119563471766 4334517597198174755784196 55347514277002246041300753686 706732537824277683009256657096704 9024267951951254836368747183136138646 115230877641678350529266029121028134305924

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 78 12554 1442358 163049190 18424290198 2081949109418 235260500483310 26584441370259454 3004041933584521614 339456738975856767914

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{113}$
The endomorphism algebra of this simple isogeny class is 4.0.1542400.2.
All geometric endomorphisms are defined over $\F_{113}$.

Base change

This is a primitive isogeny class.

Twists

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