# Properties

 Label 2.1024.aep_igf 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: $1 - 119 x + 5569 x^{2} - 121856 x^{3} + 1048576 x^{4}$ Frobenius angles: $\pm0.0188777145259$, $\pm0.169755303965$ Angle rank: $2$ (numerical) Number field: 4.0.90316457.1 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 $A(\F_{q^r})$ 932171 1096345888691 1152854296835502272 1208924807889028811300003 1267650595158211596630612968091 1329227995935821598305635840155325184 1393796574901270720524052956695323946529083 1461501637329684789938525643845344588496961539267 1532495540865806265369120370416660522183297169586341568 1606938044258986248469612525178190393960884787547718553696531

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 906 1045554 1073679231 1099510707618 1125899902339546 1152921504737736831 1180591620711572514042 1208925819613621562621634 1237940039285313556813752063 1267650600228226224696764135314

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{10}}$
 The endomorphism algebra of this simple isogeny class is 4.0.90316457.1.
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_igf $2$ (not in LMFDB)