# Properties

 Label 2.11.ai_bl 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: $( 1 - 5 x + 11 x^{2} )( 1 - 3 x + 11 x^{2} )$ Frobenius angles: $\pm0.228229222880$, $\pm0.350615407277$ Angle rank: $2$ (numerical) Jacobians: 6

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 6 curves, and hence is principally polarizable:

• $y^2=6x^6+10x^5+10x^4+7x^3+7x^2+6x+10$
• $y^2=6x^6+3x^5+5x^4+6x^3+9x^2+4x+10$
• $y^2=2x^6+9x^5+4x^3+4x+10$
• $y^2=7x^6+2x^5+8x^4+9x^3+8x^2+2x+7$
• $y^2=2x^6+2x^5+10x^4+5x^3+6x^2+6x+8$
• $y^2=2x^6+9x^5+7x^4+3x^3+7x^2+9x+2$

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 63 16065 1926288 218885625 25961811183 3135842760960 379673330311863 45949503759035625 5559893805977351568 672744554610891926625

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 4 132 1444 14948 161204 1770102 19483244 214357828 2357937724 25937214852

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{11}$
 The isogeny class factors as 1.11.af $\times$ 1.11.ad 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_h $2$ 2.121.k_hv 2.11.c_h $2$ 2.121.k_hv 2.11.i_bl $2$ 2.121.k_hv