# Properties

 Label 2.11.ah_bh Base field $\F_{11}$ Dimension $2$ $p$-rank $1$ Ordinary No 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: $1 - 7 x + 33 x^{2} - 77 x^{3} + 121 x^{4}$ Frobenius angles: $\pm0.254874969775$, $\pm0.383085442404$ Angle rank: $2$ (numerical) Number field: 4.0.21725.1 Galois group: $D_{4}$ Jacobians: 2

This isogeny class is simple and geometrically simple.

## Newton polygon

 $p$-rank: $1$ Slopes: $[0, 1/2, 1/2, 1]$

## Point counts

This isogeny class contains the Jacobians of 2 curves, and hence is principally polarizable:

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

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 71 16969 1936241 217559549 25896756976 3135209833225 379708780304981 45949647359340629 5559816583395351611 672744067024272035584

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 5 139 1451 14859 160800 1769743 19485065 214358499 2357904971 25937196054

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{11}$
 The endomorphism algebra of this simple isogeny class is 4.0.21725.1.
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_bh $2$ 2.121.r_jt