Properties

Label 2.1024.aet_iqf
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:  $1 - 123 x + 5829 x^{2} - 125952 x^{3} + 1048576 x^{4}$
Frobenius angles:  $\pm0.0662686946492$, $\pm0.107542209239$
Angle rank:  $2$ (numerical)
Number field:  4.0.1968625.1
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
$A(\F_{q^r})$ 928331 1095877107211 1152827210442336176 1208923766346577526080195 1267650570971606337270640360871 1329227996093189807217401776662515776 1393796574956846688603346914661550794465451 1461501637333560986831208898715405191727482428195 1532495540866001512756499040306694718716391808172927856 1606938044258994446510893933753087972682859439768723031461891

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 902 1045106 1073654003 1099509760338 1125899880857522 1152921504874231991 1180591620758647190078 1208925819616827877541698 1237940039285471276397239627 1267650600228232691811030426506

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{10}}$
The endomorphism algebra of this simple isogeny class is 4.0.1968625.1.
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_iqf$2$(not in LMFDB)