# Properties

 Label 3.13.ar_ff_axy Base Field $\F_{13}$ Dimension $3$ Ordinary Yes $p$-rank $3$ Principally polarizable Yes Contains a Jacobian No

## Invariants

 Base field: $\F_{13}$ Dimension: $3$ L-polynomial: $( 1 - 5 x + 13 x^{2} )( 1 - 6 x + 13 x^{2} )^{2}$ Frobenius angles: $\pm0.187167041811$, $\pm0.187167041811$, $\pm0.256122854178$ Angle rank: $2$ (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 $A(\F_{q^r})$ 576 4377600 11137367808 23969986560000 51623572937967936 112633394568133017600 247084970698469424472128 542763847693636448256000000 1192494610632200094153107018496 2619972379027192747539176403840000

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ -3 151 2304 29375 374457 4834444 62753709 815675231 10604155392 137857267711

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{13}$
 The isogeny class factors as 1.13.ag 2 $\times$ 1.13.af and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is: 1.13.ag 2 : $\mathrm{M}_{2}($$$\Q(\sqrt{-1})$$$)$ 1.13.af : $$\Q(\sqrt{-3})$$.
All geometric endomorphisms are defined over $\F_{13}$.

## 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 3.13.ah_p_ac $2$ (not in LMFDB) 3.13.af_d_by $2$ (not in LMFDB) 3.13.f_d_aby $2$ (not in LMFDB) 3.13.h_p_c $2$ (not in LMFDB) 3.13.r_ff_xy $2$ (not in LMFDB) 3.13.ao_dv_aqu $3$ (not in LMFDB) 3.13.af_aj_es $3$ (not in LMFDB) 3.13.b_g_bp $3$ (not in LMFDB) 3.13.e_y_eg $3$ (not in LMFDB) 3.13.n_da_mf $3$ (not in LMFDB)
Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 3.13.ah_p_ac $2$ (not in LMFDB) 3.13.af_d_by $2$ (not in LMFDB) 3.13.f_d_aby $2$ (not in LMFDB) 3.13.h_p_c $2$ (not in LMFDB) 3.13.r_ff_xy $2$ (not in LMFDB) 3.13.ao_dv_aqu $3$ (not in LMFDB) 3.13.af_aj_es $3$ (not in LMFDB) 3.13.b_g_bp $3$ (not in LMFDB) 3.13.e_y_eg $3$ (not in LMFDB) 3.13.n_da_mf $3$ (not in LMFDB) 3.13.ap_ej_atq $4$ (not in LMFDB) 3.13.an_dr_aqc $4$ (not in LMFDB) 3.13.ah_z_ack $4$ (not in LMFDB) 3.13.af_n_ak $4$ (not in LMFDB) 3.13.af_x_aby $4$ (not in LMFDB) 3.13.ad_f_bq $4$ (not in LMFDB) 3.13.ad_p_c $4$ (not in LMFDB) 3.13.d_f_abq $4$ (not in LMFDB) 3.13.d_p_ac $4$ (not in LMFDB) 3.13.f_n_k $4$ (not in LMFDB) 3.13.f_x_by $4$ (not in LMFDB) 3.13.h_z_ck $4$ (not in LMFDB) 3.13.n_dr_qc $4$ (not in LMFDB) 3.13.p_ej_tq $4$ (not in LMFDB) 3.13.at_gd_abcs $6$ (not in LMFDB) 3.13.an_da_amf $6$ (not in LMFDB) 3.13.al_co_akl $6$ (not in LMFDB) 3.13.ak_bz_ahg $6$ (not in LMFDB) 3.13.ai_bw_ahu $6$ (not in LMFDB) 3.13.ah_d_cs $6$ (not in LMFDB) 3.13.ae_y_aeg $6$ (not in LMFDB) 3.13.ac_d_u $6$ (not in LMFDB) 3.13.ab_ag_af $6$ (not in LMFDB) 3.13.ab_g_abp $6$ (not in LMFDB) 3.13.b_ag_f $6$ (not in LMFDB) 3.13.c_d_au $6$ (not in LMFDB) 3.13.f_aj_aes $6$ (not in LMFDB) 3.13.h_d_acs $6$ (not in LMFDB) 3.13.i_bw_hu $6$ (not in LMFDB) 3.13.k_bz_hg $6$ (not in LMFDB) 3.13.l_co_kl $6$ (not in LMFDB) 3.13.o_dv_qu $6$ (not in LMFDB) 3.13.t_gd_bcs $6$ (not in LMFDB) 3.13.af_al_eq $8$ (not in LMFDB) 3.13.af_bl_aeq $8$ (not in LMFDB) 3.13.f_al_aeq $8$ (not in LMFDB) 3.13.f_bl_eq $8$ (not in LMFDB) 3.13.ar_fd_axm $12$ (not in LMFDB) 3.13.ap_eh_ati $12$ (not in LMFDB) 3.13.am_df_anw $12$ (not in LMFDB) 3.13.al_bs_aev $12$ (not in LMFDB) 3.13.ak_ct_alg $12$ (not in LMFDB) 3.13.aj_bd_aco $12$ (not in LMFDB) 3.13.aj_bk_aep $12$ (not in LMFDB) 3.13.ai_br_age $12$ (not in LMFDB) 3.13.ah_x_acs $12$ (not in LMFDB) 3.13.ag_y_aeg $12$ (not in LMFDB) 3.13.ag_bn_aeu $12$ (not in LMFDB) 3.13.af_b_bm $12$ (not in LMFDB) 3.13.ae_t_ace $12$ (not in LMFDB) 3.13.ad_am_df $12$ (not in LMFDB) 3.13.ad_ah_dm $12$ (not in LMFDB) 3.13.ac_i_adu $12$ (not in LMFDB) 3.13.ac_x_au $12$ (not in LMFDB) 3.13.ab_ae_dl $12$ (not in LMFDB) 3.13.ab_ab_di $12$ (not in LMFDB) 3.13.a_l_abw $12$ (not in LMFDB) 3.13.a_l_bw $12$ (not in LMFDB) 3.13.b_ae_adl $12$ (not in LMFDB) 3.13.b_ab_adi $12$ (not in LMFDB) 3.13.c_i_du $12$ (not in LMFDB) 3.13.c_x_u $12$ (not in LMFDB) 3.13.d_am_adf $12$ (not in LMFDB) 3.13.d_ah_adm $12$ (not in LMFDB) 3.13.e_t_ce $12$ (not in LMFDB) 3.13.f_b_abm $12$ (not in LMFDB) 3.13.g_y_eg $12$ (not in LMFDB) 3.13.g_bn_eu $12$ (not in LMFDB) 3.13.h_x_cs $12$ (not in LMFDB) 3.13.i_br_ge $12$ (not in LMFDB) 3.13.j_bd_co $12$ (not in LMFDB) 3.13.j_bk_ep $12$ (not in LMFDB) 3.13.k_ct_lg $12$ (not in LMFDB) 3.13.l_bs_ev $12$ (not in LMFDB) 3.13.m_df_nw $12$ (not in LMFDB) 3.13.p_eh_ti $12$ (not in LMFDB) 3.13.r_fd_xm $12$ (not in LMFDB) 3.13.ah_al_gm $24$ (not in LMFDB) 3.13.ah_bl_agm $24$ (not in LMFDB) 3.13.ac_al_bw $24$ (not in LMFDB) 3.13.ac_bl_abw $24$ (not in LMFDB) 3.13.c_al_abw $24$ (not in LMFDB) 3.13.c_bl_bw $24$ (not in LMFDB) 3.13.h_al_agm $24$ (not in LMFDB) 3.13.h_bl_gm $24$ (not in LMFDB)