# Properties

 Label 2.1024.aeo_idz 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: $1 - 118 x + 5511 x^{2} - 120832 x^{3} + 1048576 x^{4}$ Frobenius angles: $\pm0.0490179712428$, $\pm0.173198423717$ Angle rank: $2$ (numerical) Number field: 4.0.6769728.2 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 $A(\F_{q^r})$ 933138 1096472609244 1152862843706930286 1208925250329445072805088 1267650614943247340626217122338 1329227996749942026292650540392994396 1393796574933509459769166868966661048538302 1461501637330954371125430872667172563240473040768 1532495540865856850861052548011877254568353283014937202 1606938044258988286468557625921048133070359336499442881737244

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 907 1045675 1073687191 1099511110015 1125899919912187 1152921505443873739 1180591620738879788359 1208925819614671735565503 1237940039285354419448715691 1267650600228227832394456806955

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{10}}$
 The endomorphism algebra of this simple isogeny class is 4.0.6769728.2.
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_idz $2$ (not in LMFDB)