# Properties

 Label 2.11.ag_bd 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

## Invariants

 Base field: $\F_{11}$ Dimension: $2$ L-polynomial: $1 - 6 x + 29 x^{2} - 66 x^{3} + 121 x^{4}$ Frobenius angles: $\pm0.268232118779$, $\pm0.423158670966$ Angle rank: $2$ (numerical) Number field: 4.0.65088.2 Galois group: $D_{4}$ Jacobians: 2

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 2 curves, and hence is principally polarizable:

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

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 79 17617 1920964 215790633 25878513559 3137418294928 379761142344271 45946314426657033 5559667500439007716 672748283643042224257

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 6 144 1440 14740 160686 1770990 19487754 214342948 2357841744 25937358624

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{11}$
 The endomorphism algebra of this simple isogeny class is 4.0.65088.2.
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.g_bd $2$ 2.121.w_lf