Properties

Label 2.1024.aep_igf
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:  $1 - 119 x + 5569 x^{2} - 121856 x^{3} + 1048576 x^{4}$
Frobenius angles:  $\pm0.0188777145259$, $\pm0.169755303965$
Angle rank:  $2$ (numerical)
Number field:  4.0.90316457.1
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
$A(\F_{q^r})$ 932171 1096345888691 1152854296835502272 1208924807889028811300003 1267650595158211596630612968091 1329227995935821598305635840155325184 1393796574901270720524052956695323946529083 1461501637329684789938525643845344588496961539267 1532495540865806265369120370416660522183297169586341568 1606938044258986248469612525178190393960884787547718553696531

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 906 1045554 1073679231 1099510707618 1125899902339546 1152921504737736831 1180591620711572514042 1208925819613621562621634 1237940039285313556813752063 1267650600228226224696764135314

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{10}}$
The endomorphism algebra of this simple isogeny class is 4.0.90316457.1.
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_igf$2$(not in LMFDB)