Properties

Label 2.1024.aep_igr
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:  $1 - 119 x + 5581 x^{2} - 121856 x^{3} + 1048576 x^{4}$
Frobenius angles:  $\pm0.0758283833176$, $\pm0.152360144022$
Angle rank:  $2$ (numerical)
Number field:  4.0.166673585.1
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
$A(\F_{q^r})$ 932183 1096371188339 1152858897304603664 1208925261029977561309715 1267650627595277929621612962723 1329227997822230522676880306280040896 1393796574995366029064026295112022746440303 1461501637333831202580196058129560939215990381635 1532495540865970385868141456559725256157367170591374544 1606938044258992134358314371305255959407729244554769895823979

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 906 1045578 1073683515 1099511119746 1125899931149446 1152921506373935751 1180591620791274340554 1208925819617051394770466 1237940039285446132297065315 1267650600228230867844253503778

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{10}}$
The endomorphism algebra of this simple isogeny class is 4.0.166673585.1.
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_igr$2$(not in LMFDB)