Properties

Label 2.1024.aep_igx
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:  $1 - 119 x + 5587 x^{2} - 121856 x^{3} + 1048576 x^{4}$
Frobenius angles:  $\pm0.103941988186$, $\pm0.134368246249$
Angle rank:  $2$ (numerical)
Number field:  4.0.7244225.1
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
$A(\F_{q^r})$ 932189 1096383838271 1152861197540961956 1208925487362970876521899 1267650643741460831144463809499 1329227998753733638851055266305005136 1393796575041074472056356839023709659799809 1461501637335782774040590814456838200575145457619 1532495540866043134200891803483885876736818208697729436 1606938044258994454310035123948421262698860643759454391418751

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 906 1045590 1073685657 1099511325594 1125899945490136 1152921507181885911 1180591620829990897734 1208925819618665696846514 1237940039285504897932267113 1267650600228232697963468005750

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{10}}$
The endomorphism algebra of this simple isogeny class is 4.0.7244225.1.
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_igx$2$(not in LMFDB)