# Properties

 Label 2.1024.aep_igp 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: $1 - 119 x + 5579 x^{2} - 121856 x^{3} + 1048576 x^{4}$ Frobenius angles: $\pm0.0680885884561$, $\pm0.156084717909$ Angle rank: $2$ (numerical) Number field: 4.0.229544337.1 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 $A(\F_{q^r})$ 932181 1096366971711 1152858130559418852 1208925185550464080581003 1267650622202498404710964394091 1329227997509996320144851222513673104 1393796574979931637078404689985060481638793 1461501637333162693973827858103938988687514807507 1532495540865944762377326979680066959518198481068102908 1606938044258991269418906515109905533367269281588002645066031

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 906 1045574 1073682801 1099511051098 1125899926359696 1152921506103115751 1180591620778200902022 1208925819616498417411954 1237940039285425433806022673 1267650600228230185527369261014

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{10}}$
 The endomorphism algebra of this simple isogeny class is 4.0.229544337.1.
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_igp $2$ (not in LMFDB)