# Properties

 Label 2.1024.aer_ilh 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: $1 - 121 x + 5701 x^{2} - 123904 x^{3} + 1048576 x^{4}$ Frobenius angles: $\pm0.0506153084167$, $\pm0.141181143239$ Angle rank: $2$ (numerical) Number field: 4.0.65148065.1 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 $A(\F_{q^r})$ 930253 1096119900659 1152842254777899244 1208924430327096945344435 1267650592857840138572971008073 1329227996548605236795547661401657536 1393796574953387883048096491535529709575573 1461501637332562239805690983391281221699683675715 1532495540865934208740175985461892195396913587817328764 1606938044258991111484005614006063577206358824640340481811579

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 904 1045338 1073668015 1099510364226 1125899900296404 1152921505269241911 1180591620755717467816 1208925819616001733365346 1237940039285416908645824215 1267650600228230060938700370178

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{10}}$
 The endomorphism algebra of this simple isogeny class is 4.0.65148065.1.
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.er_ilh $2$ (not in LMFDB)