# Properties

 Label 2.11.am_cg 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: $( 1 - 6 x + 11 x^{2} )^{2}$ Frobenius angles: $\pm0.140218899004$, $\pm0.140218899004$ 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:

• $y^2=2x^6+x^4+x^2+2$

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 36 11664 1726596 215737344 26090648676 3146721210000 380093470112196 45961377577058304 5560228769732622756 672755048952985232784

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 0 94 1296 14734 162000 1776238 19504800 214413214 2358079776 25937619454

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{11}$
 The isogeny class factors as 1.11.ag 2 and its endomorphism algebra is $\mathrm{M}_{2}($$$\Q(\sqrt{-2})$$$)$
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_ao $2$ 2.121.abc_qw 2.11.m_cg $2$ 2.121.abc_qw 2.11.g_z $3$ (not in LMFDB)
Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 2.11.a_ao $2$ 2.121.abc_qw 2.11.m_cg $2$ 2.121.abc_qw 2.11.g_z $3$ (not in LMFDB) 2.11.a_o $4$ (not in LMFDB) 2.11.ag_z $6$ (not in LMFDB) 2.11.ae_i $8$ (not in LMFDB) 2.11.e_i $8$ (not in LMFDB)