# Properties

 Label 2.11.aj_bn 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: $1 - 9 x + 39 x^{2} - 99 x^{3} + 121 x^{4}$ Frobenius angles: $\pm0.100899808413$, $\pm0.366706655625$ Angle rank: $2$ (numerical) Number field: 4.0.26533.1 Galois group: $D_{4}$ Jacobians: 1

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 1 curves, and hence is principally polarizable:

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

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 53 14257 1807247 213698173 25827579248 3136150056793 379889663866283 45961032196550133 5560271234957193833 672754159756611135232

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 3 119 1359 14595 160368 1770275 19494345 214411603 2358097785 25937585174

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{11}$
 The endomorphism algebra of this simple isogeny class is 4.0.26533.1.
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.j_bn $2$ 2.121.ad_at