# Properties

 Label 2.1024.d_absf Base field $\F_{2^{10}}$ Dimension $2$ $p$-rank $2$ Ordinary Yes Supersingular No Simple Yes Geometrically simple Yes Primitive Yes Principally polarizable Yes Contains a Jacobian Yes

## Invariants

 Base field: $\F_{2^{10}}$ Dimension: $2$ L-polynomial: $1 + 3 x - 1149 x^{2} + 3072 x^{3} + 1048576 x^{4}$ Frobenius angles: $\pm0.170249732133$, $\pm0.861797799942$ Angle rank: $2$ (numerical) Number field: 4.0.126316622340433.1 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 $A(\F_{q^r})$ 1050503 1097095959559 1152942534952668956 1208927442048880663137883 1267650625016731908452493777113 1329228000383123440463594155327000336 1393796574894308318075178919059535925417147 1461501637334533164636778167800126534414802827763 1532495540865817266243154932468519680584937766730429412 1606938044258989613574920183674983076866516080184677216782519

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 1028 1046270 1073761409 1099513103370 1125899928859238 1152921508595156279 1180591620705675129776 1208925819617632044174418 1237940039285322443249027969 1267650600228228879296783298830

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{10}}$
 The endomorphism algebra of this simple isogeny class is 4.0.126316622340433.1.
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.ad_absf $2$ (not in LMFDB)