# Properties

 Label 2.11.ak_bu 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 Yes

## Invariants

 Base field: $\F_{11}$ Dimension: $2$ L-polynomial: $( 1 - 6 x + 11 x^{2} )( 1 - 4 x + 11 x^{2} )$ Frobenius angles: $\pm0.140218899004$, $\pm0.293962833700$ Angle rank: $2$ (numerical) Jacobians: 2

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

• $y^2=2x^6+2x^4+10x^3+2x^2+2$
• $y^2=9x^5+5x^4+x^3+5x^2+9x$

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 48 13824 1839600 218087424 26026361328 3139093440000 379752329349168 45952733531602944 5560174219442900400 672760726676557161984

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 2 114 1382 14894 161602 1771938 19487302 214372894 2358056642 25937838354

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{11}$
 The isogeny class factors as 1.11.ag $\times$ 1.11.ae 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.ac_ac $2$ 2.121.ai_gc 2.11.c_ac $2$ 2.121.ai_gc 2.11.k_bu $2$ 2.121.ai_gc