# Properties

 Label 2.1024.aeo_idx 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: $1 - 118 x + 5509 x^{2} - 120832 x^{3} + 1048576 x^{4}$ Frobenius angles: $\pm0.0409105324456$, $\pm0.175390895296$ Angle rank: $2$ (numerical) Number field: 4.0.1888625.2 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 $A(\F_{q^r})$ 933136 1096468392896 1152862083407398096 1208925176318895947928320 1267650609724655848127672820496 1329227996451908141333777675583022016 1393796574918948215703783444183149873657296 1461501637330326810479494102506333267734394629120 1532495540865832538167206981719411263112886931506789136 1606938044258987428394449173710746464255390687700988896238016

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 907 1045671 1073686483 1099511042703 1125899915277147 1152921505185370551 1180591620726545934883 1208925819614152629565983 1237940039285334779811032107 1267650600228227155493338866631

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{10}}$
 The endomorphism algebra of this simple isogeny class is 4.0.1888625.2.
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.eo_idx $2$ (not in LMFDB)