# Properties

 Label 2.1024.aeo_ieh 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: $1 - 118 x + 5519 x^{2} - 120832 x^{3} + 1048576 x^{4}$ Frobenius angles: $\pm0.0764644922757$, $\pm0.162520581552$ Angle rank: $2$ (numerical) Number field: 4.0.362856000.1 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 $A(\F_{q^r})$ 933146 1096489474716 1152865884906382166 1208925546195729402430560 1267650635764470879480465984746 1329227997933570112376427758265643356 1393796574990792295605918521634012618544166 1461501637333378397312858875231934529220950015360 1532495540865947598679987441589214946540880562742314746 1606938044258991290598128595376918003778217272612870979111516

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 907 1045691 1073690023 1099511379103 1125899938405147 1152921506470507451 1180591620787400237623 1208925819616676843032063 1237940039285427724953065707 1267650600228230202234829563131

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{10}}$
 The endomorphism algebra of this simple isogeny class is 4.0.362856000.1.
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.eo_ieh $2$ (not in LMFDB)