# Properties

 Label 2.11.al_ca 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 No

## Invariants

 Base field: $\F_{11}$ Dimension: $2$ L-polynomial: $( 1 - 6 x + 11 x^{2} )( 1 - 5 x + 11 x^{2} )$ Frobenius angles: $\pm0.140218899004$, $\pm0.228229222880$ Angle rank: $2$ (numerical) Jacobians: 0

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 is principally polarizable, but does not contain a Jacobian.

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 42 12852 1802808 218484000 26131191702 3144457713600 379869675688902 45950192413776000 5559847332714983448 672747243081668428212

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 1 105 1354 14921 162251 1774962 19493321 214361041 2357918014 25937318505

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{11}$
 The isogeny class factors as 1.11.ag $\times$ 1.11.af 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.
 Twist Extension Degree Common base change 2.11.ab_ai $2$ 2.121.ar_ky 2.11.b_ai $2$ 2.121.ar_ky 2.11.l_ca $2$ 2.121.ar_ky