# Properties

 Label 2.1024.aeo_ief 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: $1 - 118 x + 5517 x^{2} - 120832 x^{3} + 1048576 x^{4}$ Frobenius angles: $\pm0.0698761161827$, $\pm0.165566469990$ Angle rank: $2$ (numerical) Number field: 4.0.28299024.1 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 $A(\F_{q^r})$ 933144 1096485258336 1152865124606320632 1208925472255545143389056 1267650630567136359416052230424 1329227997638938987557167461072547424 1393796574976615814094254062853484729725304 1461501637332785302489335105611683204920644427264 1532495540865925883965330995281375335872155186043468312 1606938044258990603403275465564646945521034187872102838567776

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 907 1045687 1073689315 1099511311855 1125899933788987 1152921506214955687 1180591620775392290707 1208925819616186246492639 1237940039285410183946258155 1267650600228229660133675659927

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{10}}$
 The endomorphism algebra of this simple isogeny class is 4.0.28299024.1.
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_ief $2$ (not in LMFDB)