Properties

Label 2.11.ah_ba
Base field $\F_{11}$
Dimension $2$
$p$-rank $2$
Ordinary Yes
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:  $1 - 7 x + 26 x^{2} - 77 x^{3} + 121 x^{4}$
Frobenius angles:  $\pm0.0895839137776$, $\pm0.469832509767$
Angle rank:  $2$ (numerical)
Number field:  4.0.40293.1
Galois group:  $D_{4}$
Jacobians:  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 the Jacobians of 4 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 64 14848 1735936 209594368 25857751744 3142960734208 379922722945984 45949122621775872 5559932695630384384 672762781232406481408

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 5 125 1304 14313 160555 1774118 19496041 214356049 2357954216 25937917565

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{11}$
The endomorphism algebra of this simple isogeny class is 4.0.40293.1.
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_ba$2$2.121.d_age