# Properties

 Label 2.11.ag_bc 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: $1 - 6 x + 28 x^{2} - 66 x^{3} + 121 x^{4}$ Frobenius angles: $\pm0.247161792509$, $\pm0.438778135579$ Angle rank: $2$ (numerical) Number field: 4.0.131904.1 Galois group: $D_{4}$ Jacobians: 10

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 10 curves, and hence is principally polarizable:

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

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 78 17316 1896102 215341776 25926727398 3140593378884 379803723796302 45943267828184064 5559516875042058942 672746366341923006276

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 6 142 1422 14710 160986 1772782 19489938 214328734 2357777862 25937284702

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{11}$
 The endomorphism algebra of this simple isogeny class is 4.0.131904.1.
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_bc $2$ 2.121.u_ja