# Properties

 Label 2.1024.aev_iuz 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: $1 - 125 x + 5953 x^{2} - 128000 x^{3} + 1048576 x^{4}$ Frobenius angles: $\pm0.0347939497301$, $\pm0.0913596598443$ Angle rank: $2$ (numerical) Number field: 4.0.400025.1 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 $A(\F_{q^r})$ 926405 1095617505275 1152809034947817620 1208922784703586848280275 1267650525453700923264392560125 1329227994195862941338804718669214400 1393796574884079420247731634646587198882445 1461501637330961327368198708122995915363073042275 1532495540865914485901113316483485111635318800364188180 1606938044258991713168567548709642114029173237990191603296875

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 900 1044858 1073637075 1099508867538 1125899840429500 1152921503228563263 1180591620697010916300 1208925819614677489634658 1237940039285400976663307475 1267650600228230535584128555498

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{10}}$
 The endomorphism algebra of this simple isogeny class is 4.0.400025.1.
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.ev_iuz $2$ (not in LMFDB)