Properties

Label 2.1024.aep_igh
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:  $1 - 119 x + 5571 x^{2} - 121856 x^{3} + 1048576 x^{4}$
Frobenius angles:  $\pm0.0331467405279$, $\pm0.167450205685$
Angle rank:  $2$ (numerical)
Number field:  4.0.217601505.1
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
$A(\F_{q^r})$ 932173 1096350105279 1152855063580018084 1208924883456498250809195 1267650600577787516087587187323 1329227996252390739499153158697039056 1393796574917201588734341569324800227835153 1461501637330398454078658512039632694594817279955 1532495540865835354211366428257500759160672989174901724 1606938044258987346167110028567610122583182339601282317018079

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 906 1045558 1073679945 1099510776346 1125899907153096 1152921505012316791 1180591620725066484294 1208925819614211891762226 1237940039285337054593388345 1267650600228227090627405674678

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{10}}$
The endomorphism algebra of this simple isogeny class is 4.0.217601505.1.
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_igh$2$(not in LMFDB)