# Properties

 Label 2.1024.aew_ixl 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: $( 1 - 63 x + 1024 x^{2} )^{2}$ Frobenius angles: $\pm0.0563432964760$, $\pm0.0563432964760$ Angle rank: $1$ (numerical)

This isogeny class is not 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 $A(\F_{q^r})$ 925444 1095488782336 1152800153499278596 1208922316379606963257344 1267650504532724409802515659524 1329227993372982245415435729892950016 1393796574855317554388413301161771679996164 1461501637330083485781733027850470549698086436864 1532495540865892738515237323732705906962768724238235396 1606938044258991405717506792985212383080903835299965529112576

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 899 1044735 1073628803 1099508441599 1125899821847939 1152921502514828031 1180591620672648668291 1208925819613951356093439 1237940039285383409264898947 1267650600228230293048006456575

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{10}}$
 The isogeny class factors as 1.1024.acl 2 and its endomorphism algebra is $\mathrm{M}_{2}($$$\Q(\sqrt{-127})$$$)$
All geometric endomorphisms are defined over $\F_{2^{10}}$.

## Base change

This is a primitive isogeny class.

## Twists

Below are some of the twists of this isogeny class.
 Twist Extension Degree Common base change 2.1024.a_acvx $2$ (not in LMFDB) 2.1024.ew_ixl $2$ (not in LMFDB) 2.1024.cl_ejh $3$ (not in LMFDB)
Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 2.1024.a_acvx $2$ (not in LMFDB) 2.1024.ew_ixl $2$ (not in LMFDB) 2.1024.cl_ejh $3$ (not in LMFDB) 2.1024.a_cvx $4$ (not in LMFDB) 2.1024.acl_ejh $6$ (not in LMFDB)