# Properties

 Label 2.1024.aeq_iiv 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: $1 - 120 x + 5637 x^{2} - 122880 x^{3} + 1048576 x^{4}$ Frobenius angles: $\pm0.0465577460529$, $\pm0.153694224197$ Angle rank: $2$ (numerical) Number field: 4.0.148733200.1 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 $A(\F_{q^r})$ 931214 1096238157796 1152849222928853894 1208924710830625721915200 1267650600427513433128114212254 1329227996605045932098933142443255236 1393796574944807089426295342845387121303894 1461501637331862619889241368314470673068944467200 1532495540865898174717082998338799220635769025026071214 1606938044258989636911256854008905724430248227621980494260516

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 905 1045451 1073674505 1099510619343 1125899907019625 1152921505318196411 1180591620748449252905 1208925819615423021334303 1237940039285387800593778505 1267650600228228897705906969131

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{10}}$
 The endomorphism algebra of this simple isogeny class is 4.0.148733200.1.
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.eq_iiv $2$ (not in LMFDB)