# Properties

 Label 2.1024.aet_iqf 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: $1 - 123 x + 5829 x^{2} - 125952 x^{3} + 1048576 x^{4}$ Frobenius angles: $\pm0.0662686946492$, $\pm0.107542209239$ Angle rank: $2$ (numerical) Number field: 4.0.1968625.1 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 $A(\F_{q^r})$ 928331 1095877107211 1152827210442336176 1208923766346577526080195 1267650570971606337270640360871 1329227996093189807217401776662515776 1393796574956846688603346914661550794465451 1461501637333560986831208898715405191727482428195 1532495540866001512756499040306694718716391808172927856 1606938044258994446510893933753087972682859439768723031461891

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 902 1045106 1073654003 1099509760338 1125899880857522 1152921504874231991 1180591620758647190078 1208925819616827877541698 1237940039285471276397239627 1267650600228232691811030426506

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{10}}$
 The endomorphism algebra of this simple isogeny class is 4.0.1968625.1.
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_iqf $2$ (not in LMFDB)