Properties

Label 2.1024.aet_iqd
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:  $1 - 123 x + 5827 x^{2} - 125952 x^{3} + 1048576 x^{4}$
Frobenius angles:  $\pm0.0470279964326$, $\pm0.117385164674$
Angle rank:  $2$ (numerical)
Number field:  4.0.7983729.1
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
$A(\F_{q^r})$ 928329 1095872889591 1152826417916319852 1208923684533821277095931 1267650564743904294558070684599 1329227995702039436965344786746789904 1393796574935420031592848740252355253118709 1461501637332504941699191455938210738813437596339 1532495540865953802753450346324186333309554323398229652 1606938044258992448632080051537164375424844306965330892732551

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 902 1045102 1073653265 1099509685930 1125899875326212 1152921504534963127 1180591620740498105642 1208925819615954337482514 1237940039285432736563697905 1267650600228231115762540785502

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{10}}$
The endomorphism algebra of this simple isogeny class is 4.0.7983729.1.
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.et_iqd$2$(not in LMFDB)