# Properties

 Label 2.1024.aeo_ieb 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: $( 1 - 63 x + 1024 x^{2} )( 1 - 55 x + 1024 x^{2} )$ Frobenius angles: $\pm0.0563432964760$, $\pm0.170852887823$ Angle rank: $2$ (numerical)

This isogeny class is not 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 $A(\F_{q^r})$ 933140 1096476825600 1152863604006594740 1208925324322402979635200 1267650620156524589999853487700 1329227997047125055195815486525593600 1393796574947974442983975163410221867832820 1461501637331573299763214192163763147939396812800 1532495540865880511657306041893146816700190801628837780 1606938044258989101532163583811376482392102545967632029440000

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 907 1045679 1073687899 1099511177311 1125899924542507 1152921505701638927 1180591620751132105723 1208925819615183701335231 1237940039285373532487718091 1267650600228228475366270815599

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{10}}$
 The isogeny class factors as 1.1024.acl $\times$ 1.1024.acd and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is:
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.ai_accn $2$ (not in LMFDB) 2.1024.i_accn $2$ (not in LMFDB) 2.1024.eo_ieb $2$ (not in LMFDB)