# Properties

 Label 2.1024.aep_igl Base Field $\F_{2^{10}}$ Dimension $2$ Ordinary Yes $p$-rank $2$ Principally polarizable Yes Contains a Jacobian Yes

## Invariants

 Base field: $\F_{2^{10}}$ Dimension: $2$ L-polynomial: $1 - 119 x + 5575 x^{2} - 121856 x^{3} + 1048576 x^{4}$ Frobenius angles: $\pm0.0522393759971$, $\pm0.162294262785$ Angle rank: $2$ (numerical) Number field: 4.0.6115193.1 Galois group: $D_{4}$

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 a Jacobian, and hence is principally polarizable.

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 932177 1096358538479 1152856597069450868 1208925034538663549207867 1267650611400861518217822106947 1329227996882927505286597699313259824 1393796574948765203396239934521259481246701 1461501637331798636238356369806990640877693338003 1532495540865891444434155656094841993656666240800289916 1606938044258989400896026340230302749968581469368026388771559

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 906 1045566 1073681373 1099510913754 1125899916765916 1152921505559220255 1180591620751801905846 1208925819615370095298770 1237940039285382363914526069 1267650600228228711522718580086

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{10}}$
 The endomorphism algebra of this simple isogeny class is 4.0.6115193.1.
All geometric endomorphisms are defined over $\F_{2^{10}}$.

## Base change

This is a primitive isogeny class.

## Twists

Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 2.1024.ep_igl $2$ (not in LMFDB)