# Properties

 Label 2.11.ah_bd 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: $1 - 7 x + 29 x^{2} - 77 x^{3} + 121 x^{4}$ Frobenius angles: $\pm0.162126013132$, $\pm0.441671623734$ Angle rank: $2$ (numerical) Number field: 4.0.196245.1 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:

• $y^2=8x^6+2x^5+5x^4+5x^3+5x^2+6x+6$
• $y^2=2x^6+9x^5+10x^4+8x^3+3x^2+10x+1$

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 67 15745 1820725 213329005 25941832912 3145275126625 380071732355137 45952810361641845 5559718341588279775 672744727725974368000

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 5 131 1367 14571 161080 1775423 19503685 214373251 2357863307 25937221526

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{11}$
 The endomorphism algebra of this simple isogeny class is 4.0.196245.1.
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_bd $2$ 2.121.j_f