Properties

Label 2.11.ai_bk
Base Field $\F_{11}$
Dimension $2$
Ordinary Yes
$p$-rank $2$
Principally polarizable Yes
Contains a Jacobian Yes

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Invariants

Base field:  $\F_{11}$
Dimension:  $2$
L-polynomial:  $1 - 8 x + 36 x^{2} - 88 x^{3} + 121 x^{4}$
Frobenius angles:  $\pm0.196063835166$, $\pm0.372536541753$
Angle rank:  $2$ (numerical)
Number field:  4.0.35072.1
Galois group:  $D_{4}$
Jacobians:  2

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 2 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 62 15748 1892798 217259408 25948758382 3138951848068 379874132864078 45954654361751552 5559850292795022878 672736271248784205508

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 4 130 1420 14838 161124 1771858 19493548 214381854 2357919268 25936895490

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{11}$
The endomorphism algebra of this simple isogeny class is 4.0.35072.1.
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.i_bk$2$2.121.i_fa