Properties

Label 2.1024.aeo_ieh
Base Field $\F_{2^{10}}$
Dimension $2$
Ordinary Yes
$p$-rank $2$
Principally polarizable Yes
Contains a Jacobian Yes

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Invariants

Base field:  $\F_{2^{10}}$
Dimension:  $2$
L-polynomial:  $1 - 118 x + 5519 x^{2} - 120832 x^{3} + 1048576 x^{4}$
Frobenius angles:  $\pm0.0764644922757$, $\pm0.162520581552$
Angle rank:  $2$ (numerical)
Number field:  4.0.362856000.1
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.

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 933146 1096489474716 1152865884906382166 1208925546195729402430560 1267650635764470879480465984746 1329227997933570112376427758265643356 1393796574990792295605918521634012618544166 1461501637333378397312858875231934529220950015360 1532495540865947598679987441589214946540880562742314746 1606938044258991290598128595376918003778217272612870979111516

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 907 1045691 1073690023 1099511379103 1125899938405147 1152921506470507451 1180591620787400237623 1208925819616676843032063 1237940039285427724953065707 1267650600228230202234829563131

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{10}}$
The endomorphism algebra of this simple isogeny class is 4.0.362856000.1.
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.
TwistExtension DegreeCommon base change
2.1024.eo_ieh$2$(not in LMFDB)