# Properties

 Label 2.1024.aeq_iix 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: $( 1 - 63 x + 1024 x^{2} )( 1 - 57 x + 1024 x^{2} )$ Frobenius angles: $\pm0.0563432964760$, $\pm0.150267280813$ 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 $A(\F_{q^r})$ 931216 1096242374656 1152849996118925104 1208924787902243336331264 1267650606031793288026545428176 1329227996937475653166295557364770816 1393796574961795566447621668617760484179056 1461501637332633392849077637618121722829985972224 1532495540865929758892457863589398992476473178068594704 1606938044258990816661176912609456593530688303408756796286976

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 905 1045455 1073675225 1099510689439 1125899911997225 1152921505606533231 1180591620762839052665 1208925819616060589783359 1237940039285413314087463625 1267650600228229828364496840975

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{10}}$
 The isogeny class factors as 1.1024.acl $\times$ 1.1024.acf 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.ag_achj $2$ (not in LMFDB) 2.1024.g_achj $2$ (not in LMFDB) 2.1024.eq_iix $2$ (not in LMFDB)