# Properties

 Label 2.1024.aep_igr 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: $1 - 119 x + 5581 x^{2} - 121856 x^{3} + 1048576 x^{4}$ Frobenius angles: $\pm0.0758283833176$, $\pm0.152360144022$ Angle rank: $2$ (numerical) Number field: 4.0.166673585.1 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 $A(\F_{q^r})$ 932183 1096371188339 1152858897304603664 1208925261029977561309715 1267650627595277929621612962723 1329227997822230522676880306280040896 1393796574995366029064026295112022746440303 1461501637333831202580196058129560939215990381635 1532495540865970385868141456559725256157367170591374544 1606938044258992134358314371305255959407729244554769895823979

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 906 1045578 1073683515 1099511119746 1125899931149446 1152921506373935751 1180591620791274340554 1208925819617051394770466 1237940039285446132297065315 1267650600228230867844253503778

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{10}}$
 The endomorphism algebra of this simple isogeny class is 4.0.166673585.1.
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_igr $2$ (not in LMFDB)