Properties

Label 2.1024.aep_igp
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:  $1 - 119 x + 5579 x^{2} - 121856 x^{3} + 1048576 x^{4}$
Frobenius angles:  $\pm0.0680885884561$, $\pm0.156084717909$
Angle rank:  $2$ (numerical)
Number field:  4.0.229544337.1
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
$A(\F_{q^r})$ 932181 1096366971711 1152858130559418852 1208925185550464080581003 1267650622202498404710964394091 1329227997509996320144851222513673104 1393796574979931637078404689985060481638793 1461501637333162693973827858103938988687514807507 1532495540865944762377326979680066959518198481068102908 1606938044258991269418906515109905533367269281588002645066031

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 906 1045574 1073682801 1099511051098 1125899926359696 1152921506103115751 1180591620778200902022 1208925819616498417411954 1237940039285425433806022673 1267650600228230185527369261014

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{10}}$
The endomorphism algebra of this simple isogeny class is 4.0.229544337.1.
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.ep_igp$2$(not in LMFDB)