# Properties

 Label 2.11.ah_bb Base Field $\F_{11}$ Dimension $2$ Ordinary Yes $p$-rank $2$ Principally polarizable Yes Contains a Jacobian Yes

## Invariants

 Base field: $\F_{11}$ Dimension: $2$ L-polynomial: $1 - 7 x + 27 x^{2} - 77 x^{3} + 121 x^{4}$ Frobenius angles: $\pm0.116678659763$, $\pm0.461158112795$ Angle rank: $2$ (numerical) Number field: 4.0.206045.1 Galois group: $D_{4}$ Jacobians: 4

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 4 curves, and hence is principally polarizable:

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

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 65 15145 1764035 210894125 25897066000 3144715205905 380023969959335 45952353789519125 5559939576013933565 672760097642165728000

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 5 127 1325 14403 160800 1775107 19501235 214371123 2357957135 25937814102

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{11}$
 The endomorphism algebra of this simple isogeny class is 4.0.206045.1.
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.h_bb $2$ 2.121.f_aed