# Properties

 Label 2.1024.aep_igt 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: $1 - 119 x + 5583 x^{2} - 121856 x^{3} + 1048576 x^{4}$ Frobenius angles: $\pm0.0838690408520$, $\pm0.147968261758$ Angle rank: $2$ (numerical) Number field: 4.0.100858905.2 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 6 7 8 9 10 $A(\F_{q^r})$ 932185 1096375404975 1152859664049922420 1208925336491899853494875 1267650632982698175656594386675 1329227998133598069518230666885724400 1393796575010701267419041697552539607365605 1461501637334490711755911569058888800677655529875 1532495540865995321236935852049709416525850099971048540 1606938044258992953352200417308664640425951787166499766824375

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 906 1045582 1073684229 1099511188378 1125899935934436 1152921506644004047 1180591620804263792694 1208925819617596927974418 1237940039285466274927566861 1267650600228231513916511820502

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{10}}$
 The endomorphism algebra of this simple isogeny class is 4.0.100858905.2.
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.
 Twist Extension Degree Common base change 2.1024.ep_igt $2$ (not in LMFDB)