Properties

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

Learn more about

Invariants

Base field:  $\F_{2^{10}}$
Dimension:  $2$
L-polynomial:  $1 - 124 x + 5889 x^{2} - 126976 x^{3} + 1048576 x^{4}$
Frobenius angles:  $\pm0.0291375480534$, $\pm0.109240146068$
Angle rank:  $2$ (numerical)
Number field:  4.0.2285712.4
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
$A(\F_{q^r})$ 927366 1095744135156 1152817523430853302 1208923212946046562938688 1267650543375460409381633831766 1329227994834738974955799061949484404 1393796574903078701099818055267181666934758 1461501637331378630035236046529752290155152157952 1532495540865916664252951335153370689501572525740711718 1606938044258991270832080444182667648147402174596484246384756

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 901 1044979 1073644981 1099509257023 1125899856347221 1152921503782699891 1180591620713103933157 1208925819615022674310399 1237940039285402736321908773 1267650600228230186642166925939

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{10}}$
The endomorphism algebra of this simple isogeny class is 4.0.2285712.4.
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.eu_isn$2$(not in LMFDB)