# Properties

 Label 2.1024.aet_iqd 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: $1 - 123 x + 5827 x^{2} - 125952 x^{3} + 1048576 x^{4}$ Frobenius angles: $\pm0.0470279964326$, $\pm0.117385164674$ Angle rank: $2$ (numerical) Number field: 4.0.7983729.1 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 $A(\F_{q^r})$ 928329 1095872889591 1152826417916319852 1208923684533821277095931 1267650564743904294558070684599 1329227995702039436965344786746789904 1393796574935420031592848740252355253118709 1461501637332504941699191455938210738813437596339 1532495540865953802753450346324186333309554323398229652 1606938044258992448632080051537164375424844306965330892732551

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 902 1045102 1073653265 1099509685930 1125899875326212 1152921504534963127 1180591620740498105642 1208925819615954337482514 1237940039285432736563697905 1267650600228231115762540785502

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{10}}$
 The endomorphism algebra of this simple isogeny class is 4.0.7983729.1.
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.et_iqd $2$ (not in LMFDB)