Properties

Label 2.1024.aep_igj
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:  $1 - 119 x + 5573 x^{2} - 121856 x^{3} + 1048576 x^{4}$
Frobenius angles:  $\pm0.0434335197957$, $\pm0.164975321647$
Angle rank:  $2$ (numerical)
Number field:  4.0.31498265.1
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
$A(\F_{q^r})$ 932175 1096354321875 1152855830324667600 1208924959006376496421875 1267650605992004156612933305875 1329227996568092671599294025296600000 1393796574933033067290145318726381736798775 1461501637331103065991543433503572592582077671875 1532495540865863746682784946130141971937834761976125200 1606938044258988396908441560388267156120225591523614208046875

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 906 1045562 1073680659 1099510845058 1125899911961886 1152921505286144567 1180591620738476268234 1208925819614794733075938 1237940039285359989849149931 1267650600228227919516163620002

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{10}}$
The endomorphism algebra of this simple isogeny class is 4.0.31498265.1.
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_igj$2$(not in LMFDB)