# Properties

 Label 2.1024.aep_igh 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: $1 - 119 x + 5571 x^{2} - 121856 x^{3} + 1048576 x^{4}$ Frobenius angles: $\pm0.0331467405279$, $\pm0.167450205685$ Angle rank: $2$ (numerical) Number field: 4.0.217601505.1 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 $A(\F_{q^r})$ 932173 1096350105279 1152855063580018084 1208924883456498250809195 1267650600577787516087587187323 1329227996252390739499153158697039056 1393796574917201588734341569324800227835153 1461501637330398454078658512039632694594817279955 1532495540865835354211366428257500759160672989174901724 1606938044258987346167110028567610122583182339601282317018079

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 906 1045558 1073679945 1099510776346 1125899907153096 1152921505012316791 1180591620725066484294 1208925819614211891762226 1237940039285337054593388345 1267650600228227090627405674678

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{10}}$
 The endomorphism algebra of this simple isogeny class is 4.0.217601505.1.
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_igh $2$ (not in LMFDB)