Properties

Label 2.11.ag_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:  $1 - 6 x + 26 x^{2} - 66 x^{3} + 121 x^{4}$
Frobenius angles:  $\pm0.210408938282$, $\pm0.463259653430$
Angle rank:  $2$ (numerical)
Number field:  4.0.18000.1
Galois group:  $C_4$
Jacobians:  12

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 12 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 76 16720 1846876 214283520 25994412316 3145266765520 379888898840716 45942527257989120 5559503633396462956 672745463572852450000

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 6 138 1386 14638 161406 1775418 19494306 214325278 2357772246 25937249898

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{11}$
The endomorphism algebra of this simple isogeny class is 4.0.18000.1.
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.g_ba$2$2.121.q_ew