# Properties

 Label 3.11.ao_dr_apf 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: $( 1 - 3 x + 11 x^{2} )( 1 - 11 x + 51 x^{2} - 121 x^{3} + 121 x^{4} )$ Frobenius angles: $\pm0.0215640055172$, $\pm0.270299311731$, $\pm0.350615407277$ Angle rank: $3$ (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 $A(\F_{q^r})$ 369 1688175 2464372404 3154133836575 4152184991334864 5541238200229477200 7393628399371374078819 9848506476570552624992175 13109914968524435938233985524 17449358250960962865742500000000

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ -2 116 1393 14716 160083 1765601 19469728 214332196 2357933443 25937359171

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{11}$
 The isogeny class factors as 1.11.ad $\times$ 2.11.al_bz and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is:
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.ai_bd_adl $2$ (not in LMFDB) 3.11.i_bd_dl $2$ (not in LMFDB) 3.11.o_dr_pf $2$ (not in LMFDB)
Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 3.11.ai_bd_adl $2$ (not in LMFDB) 3.11.i_bd_dl $2$ (not in LMFDB) 3.11.o_dr_pf $2$ (not in LMFDB) 3.11.ae_f_f $5$ (not in LMFDB) 3.11.ae_bj_adh $5$ (not in LMFDB) 3.11.b_f_cs $5$ (not in LMFDB) 3.11.g_z_cx $5$ (not in LMFDB) 3.11.am_db_amj $10$ (not in LMFDB) 3.11.ah_bd_aec $10$ (not in LMFDB) 3.11.ag_z_acx $10$ (not in LMFDB) 3.11.ac_ab_bx $10$ (not in LMFDB) 3.11.ac_bd_abp $10$ (not in LMFDB) 3.11.ab_f_acs $10$ (not in LMFDB) 3.11.c_ab_abx $10$ (not in LMFDB) 3.11.c_bd_bp $10$ (not in LMFDB) 3.11.e_f_af $10$ (not in LMFDB) 3.11.e_bj_dh $10$ (not in LMFDB) 3.11.h_bd_ec $10$ (not in LMFDB) 3.11.m_db_mj $10$ (not in LMFDB)