# Properties

 Label 3.11.as_fl_axo Base Field $\F_{11}$ Dimension $3$ Ordinary Yes $p$-rank $3$ Principally polarizable Yes Contains a Jacobian No

## Invariants

 Base field: $\F_{11}$ Dimension: $3$ L-polynomial: $( 1 - 6 x + 11 x^{2} )^{3}$ Frobenius angles: $\pm0.140218899004$, $\pm0.140218899004$, $\pm0.140218899004$ Angle rank: $1$ (numerical)

This isogeny class is not simple.

## Newton polygon

This isogeny class is ordinary.

 $p$-rank: $3$ Slopes: $[0, 0, 0, 1, 1, 1]$

## Point counts

This isogeny class is principally polarizable, but does not contain a Jacobian.

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 216 1259712 2268747144 3168750108672 4214318118039576 5581968754419000000 7410296971998791645256 9853478099381345260142592 13111095803211447966488930904 17449598901666272811693707765952

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ -6 80 1278 14780 162474 1778576 19513614 214440380 2358145818 25937716880

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{11}$
 The isogeny class factors as 1.11.ag 3 and its endomorphism algebra is $\mathrm{M}_{3}($$$\Q(\sqrt{-2})$$$)$
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 3.11.ag_ad_dg $2$ (not in LMFDB) 3.11.g_ad_adg $2$ (not in LMFDB) 3.11.s_fl_xo $2$ (not in LMFDB) 3.11.a_a_as $3$ (not in LMFDB)
Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 3.11.ag_ad_dg $2$ (not in LMFDB) 3.11.g_ad_adg $2$ (not in LMFDB) 3.11.s_fl_xo $2$ (not in LMFDB) 3.11.a_a_as $3$ (not in LMFDB) 3.11.ag_z_adg $4$ (not in LMFDB) 3.11.g_z_dg $4$ (not in LMFDB) 3.11.am_cu_akw $6$ (not in LMFDB) 3.11.a_a_s $6$ (not in LMFDB) 3.11.m_cu_kw $6$ (not in LMFDB) 3.11.ak_br_afg $8$ (not in LMFDB) 3.11.ac_af_bo $8$ (not in LMFDB) 3.11.c_af_abo $8$ (not in LMFDB) 3.11.k_br_fg $8$ (not in LMFDB)