# Properties

 Label 2.1024.ai_agd Base field $\F_{2^{10}}$ Dimension $2$ $p$-rank $2$ Ordinary yes Supersingular no Simple yes Geometrically simple yes Primitive yes Principally polarizable yes Contains a Jacobian yes

## Invariants

 Base field: $\F_{2^{10}}$ Dimension: $2$ L-polynomial: $1 - 8 x - 159 x^{2} - 8192 x^{3} + 1048576 x^{4}$ Frobenius angles: $\pm0.205257621131$, $\pm0.735510757239$ Angle rank: $2$ (numerical) Number field: 4.0.149350032.2 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.

$r$ $1$ $2$ $3$ $4$ $5$
$A(\F_{q^r})$ $1040218$ $1099113062724$ $1152890470103202106$ $1208930038224502123323648$ $1267650635534099477144686846138$

$r$ $1$ $2$ $3$ $4$ $5$ $6$ $7$ $8$ $9$ $10$
$C(\F_{q^r})$ $1017$ $1048195$ $1073712921$ $1099515464575$ $1125899938200537$ $1152921505631535619$ $1180591620792333810489$ $1208925819611625189972223$ $1237940039285343668795297721$ $1267650600228228170315560289155$

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{10}}$
 The endomorphism algebra of this simple isogeny class is 4.0.149350032.2.
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.
TwistExtension degreeCommon base change
2.1024.i_agd$2$(not in LMFDB)