# Properties

 Label 2.1024.aeo_ied 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: $1 - 118 x + 5515 x^{2} - 120832 x^{3} + 1048576 x^{4}$ Frobenius angles: $\pm0.0632249866452$, $\pm0.168323205285$ Angle rank: $2$ (numerical) Number field: 4.0.521407040.1 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 $A(\F_{q^r})$ 933142 1096481041964 1152864364306391506 1208925398297769669476960 1267650625364487596259491725702 1329227997343457338723808938609812236 1393796574962343212156305252608751468838242 1461501637332183606761829831363460481767374227840 1532495540865903522158167219540915505573041270568357686 1606938044258989873779154562440114395741872241598626061461804

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 907 1045683 1073688607 1099511244591 1125899929168107 1152921505958666211 1180591620763302926623 1208925819615688535452191 1237940039285392120222285963 1267650600228229084561731173203

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{10}}$
 The endomorphism algebra of this simple isogeny class is 4.0.521407040.1.
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_ied $2$ (not in LMFDB)