# Properties

 Label 2.11.ak_bv Base field $\F_{11}$ Dimension $2$ $p$-rank $2$ Ordinary Yes Supersingular No Simple No Geometrically simple No Primitive Yes Principally polarizable Yes Contains a Jacobian Yes

## Invariants

 Base field: $\F_{11}$ Dimension: $2$ L-polynomial: $( 1 - 5 x + 11 x^{2} )^{2}$ Frobenius angles: $\pm0.228229222880$, $\pm0.228229222880$ Angle rank: $1$ (numerical) Jacobians: 1

This isogeny class is not 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:

• $y^2=2x^6+2x^5+x^3+2x+2$

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 49 14161 1882384 221265625 26171797729 3142195845376 379646013033049 45939009972515625 5559465921864288784 672739437300921924241

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 2 116 1412 15108 162502 1773686 19481842 214308868 2357756252 25937017556

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{11}$
 The isogeny class factors as 1.11.af 2 and its endomorphism algebra is $\mathrm{M}_{2}($$$\Q(\sqrt{-19})$$$)$
All geometric endomorphisms are defined over $\F_{11}$.

## Base change

This is a primitive isogeny class.

## Twists

Below are some of the twists of this isogeny class.
 Twist Extension Degree Common base change 2.11.a_ad $2$ 2.121.ag_jr 2.11.k_bv $2$ 2.121.ag_jr 2.11.f_o $3$ (not in LMFDB)
Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 2.11.a_ad $2$ 2.121.ag_jr 2.11.k_bv $2$ 2.121.ag_jr 2.11.f_o $3$ (not in LMFDB) 2.11.a_d $4$ (not in LMFDB) 2.11.af_o $6$ (not in LMFDB)