Properties

Label 2.1024.aeo_ieb
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:  $( 1 - 63 x + 1024 x^{2} )( 1 - 55 x + 1024 x^{2} )$
Frobenius angles:  $\pm0.0563432964760$, $\pm0.170852887823$
Angle rank:  $2$ (numerical)

This isogeny class is not 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
$A(\F_{q^r})$ 933140 1096476825600 1152863604006594740 1208925324322402979635200 1267650620156524589999853487700 1329227997047125055195815486525593600 1393796574947974442983975163410221867832820 1461501637331573299763214192163763147939396812800 1532495540865880511657306041893146816700190801628837780 1606938044258989101532163583811376482392102545967632029440000

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 907 1045679 1073687899 1099511177311 1125899924542507 1152921505701638927 1180591620751132105723 1208925819615183701335231 1237940039285373532487718091 1267650600228228475366270815599

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{10}}$
The isogeny class factors as 1.1024.acl $\times$ 1.1024.acd and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is:
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.ai_accn$2$(not in LMFDB)
2.1024.i_accn$2$(not in LMFDB)
2.1024.eo_ieb$2$(not in LMFDB)