Properties

Label 2.11.ai_bl
Base field $\F_{11}$
Dimension $2$
$p$-rank $2$
Ordinary Yes
Supersingular No
Simple No
Geometrically simple No
Primitive Yes
Principally polarizable Yes
Contains a Jacobian Yes

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Invariants

Base field:  $\F_{11}$
Dimension:  $2$
L-polynomial:  $( 1 - 5 x + 11 x^{2} )( 1 - 3 x + 11 x^{2} )$
Frobenius angles:  $\pm0.228229222880$, $\pm0.350615407277$
Angle rank:  $2$ (numerical)
Jacobians:  6

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 the Jacobians of 6 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 63 16065 1926288 218885625 25961811183 3135842760960 379673330311863 45949503759035625 5559893805977351568 672744554610891926625

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 4 132 1444 14948 161204 1770102 19483244 214357828 2357937724 25937214852

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{11}$
The isogeny class factors as 1.11.af $\times$ 1.11.ad 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 $\F_{11}$.

Base change

This is a primitive isogeny class.

Twists

Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.11.ac_h$2$2.121.k_hv
2.11.c_h$2$2.121.k_hv
2.11.i_bl$2$2.121.k_hv