Properties

Label 2.11.ah_bh
Base field $\F_{11}$
Dimension $2$
$p$-rank $1$
Ordinary No
Supersingular No
Simple Yes
Geometrically simple Yes
Primitive Yes
Principally polarizable Yes
Contains a Jacobian Yes

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Invariants

Base field:  $\F_{11}$
Dimension:  $2$
L-polynomial:  $1 - 7 x + 33 x^{2} - 77 x^{3} + 121 x^{4}$
Frobenius angles:  $\pm0.254874969775$, $\pm0.383085442404$
Angle rank:  $2$ (numerical)
Number field:  4.0.21725.1
Galois group:  $D_{4}$
Jacobians:  2

This isogeny class is simple and geometrically simple.

Newton polygon

$p$-rank:  $1$
Slopes:  $[0, 1/2, 1/2, 1]$

Point counts

This isogeny class contains the Jacobians of 2 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 71 16969 1936241 217559549 25896756976 3135209833225 379708780304981 45949647359340629 5559816583395351611 672744067024272035584

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 5 139 1451 14859 160800 1769743 19485065 214358499 2357904971 25937196054

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{11}$
The endomorphism algebra of this simple isogeny class is 4.0.21725.1.
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.h_bh$2$2.121.r_jt