# Properties

 Label 2.1024.aet_iqb 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: $1 - 123 x + 5825 x^{2} - 125952 x^{3} + 1048576 x^{4}$ Frobenius angles: $\pm0.0257138497233$, $\pm0.123950606712$ Angle rank: $2$ (numerical) Number field: 4.0.6943545.3 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 $A(\F_{q^r})$ 928327 1095868671979 1152825625390443376 1208923602703473942554355 1267650558510662829835012783327 1329227995309955670707109622094992576 1393796574913881146022344592084490066511407 1461501637331438092823749357834982650227544994595 1532495540865905207768525277438960148902221440608357616 1606938044258990386745785105504204688429631251651199596789179

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 902 1045098 1073652527 1099509611506 1125899869789982 1152921504194884671 1180591620722253959918 1208925819615071860776226 1237940039285393481847489583 1267650600228229489221051691578

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{10}}$
 The endomorphism algebra of this simple isogeny class is 4.0.6943545.3.
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.et_iqb $2$ (not in LMFDB)