# Properties

 Label 2.11.ag_be 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: $( 1 - 4 x + 11 x^{2} )( 1 - 2 x + 11 x^{2} )$ Frobenius angles: $\pm0.293962833700$, $\pm0.402508885479$ Angle rank: $2$ (numerical) Jacobians: 4

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 4 curves, and hence is principally polarizable:

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

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 80 17920 1946000 216186880 25820762000 3133713856000 379725137379920 45951745826488320 5559932468814626000 672749871005722048000

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 6 146 1458 14766 160326 1768898 19485906 214368286 2357954118 25937419826

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{11}$
 The isogeny class factors as 1.11.ae $\times$ 1.11.ac 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_o $2$ 2.121.y_nm 2.11.c_o $2$ 2.121.y_nm 2.11.g_be $2$ 2.121.y_nm