# Properties

 Label 3.13.aq_eq_auw 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: $( 1 - 7 x + 13 x^{2} )( 1 - 6 x + 13 x^{2} )( 1 - 3 x + 13 x^{2} )$ Frobenius angles: $\pm0.0772104791556$, $\pm0.187167041811$, $\pm0.363422825076$ 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 $A(\F_{q^r})$ 616 4398240 10789402624 23377613212800 51150534515943016 112452094830577582080 247116075883767141604168 542851238517134881136140800 1192549190986974855482957436928 2619987533557127401286211408631200

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ -2 154 2236 28658 371038 4826668 62761606 815806562 10604640748 137858065114

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{13}$
 The isogeny class factors as 1.13.ah $\times$ 1.13.ag $\times$ 1.13.ad 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 $\F_{13}$.

## 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.ak_bq_afe $2$ (not in LMFDB) 3.13.ae_a_w $2$ (not in LMFDB) 3.13.ac_ag_cw $2$ (not in LMFDB) 3.13.c_ag_acw $2$ (not in LMFDB) 3.13.e_a_aw $2$ (not in LMFDB) 3.13.k_bq_fe $2$ (not in LMFDB) 3.13.q_eq_uw $2$ (not in LMFDB) 3.13.ah_bn_afq $3$ (not in LMFDB) 3.13.ae_m_ao $3$ (not in LMFDB)
Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 3.13.ak_bq_afe $2$ (not in LMFDB) 3.13.ae_a_w $2$ (not in LMFDB) 3.13.ac_ag_cw $2$ (not in LMFDB) 3.13.c_ag_acw $2$ (not in LMFDB) 3.13.e_a_aw $2$ (not in LMFDB) 3.13.k_bq_fe $2$ (not in LMFDB) 3.13.q_eq_uw $2$ (not in LMFDB) 3.13.ah_bn_afq $3$ (not in LMFDB) 3.13.ae_m_ao $3$ (not in LMFDB) 3.13.ao_dw_arg $4$ (not in LMFDB) 3.13.ai_bi_aeu $4$ (not in LMFDB) 3.13.ag_u_acu $4$ (not in LMFDB) 3.13.a_c_adg $4$ (not in LMFDB) 3.13.a_c_dg $4$ (not in LMFDB) 3.13.g_u_cu $4$ (not in LMFDB) 3.13.i_bi_eu $4$ (not in LMFDB) 3.13.o_dw_rg $4$ (not in LMFDB) 3.13.ao_dy_arm $6$ (not in LMFDB) 3.13.al_cx_amk $6$ (not in LMFDB) 3.13.ai_bk_aeo $6$ (not in LMFDB) 3.13.af_bb_adq $6$ (not in LMFDB) 3.13.ac_g_bm $6$ (not in LMFDB) 3.13.ab_p_ack $6$ (not in LMFDB) 3.13.b_p_ck $6$ (not in LMFDB) 3.13.c_g_abm $6$ (not in LMFDB) 3.13.e_m_o $6$ (not in LMFDB) 3.13.f_bb_dq $6$ (not in LMFDB) 3.13.h_bn_fq $6$ (not in LMFDB) 3.13.i_bk_eo $6$ (not in LMFDB) 3.13.l_cx_mk $6$ (not in LMFDB) 3.13.o_dy_rm $6$ (not in LMFDB) 3.13.am_di_aoi $12$ (not in LMFDB) 3.13.aj_cn_ajy $12$ (not in LMFDB) 3.13.ag_bg_ads $12$ (not in LMFDB) 3.13.af_bl_aec $12$ (not in LMFDB) 3.13.ae_w_abs $12$ (not in LMFDB) 3.13.ad_bd_acc $12$ (not in LMFDB) 3.13.ac_q_i $12$ (not in LMFDB) 3.13.ab_z_ac $12$ (not in LMFDB) 3.13.b_z_c $12$ (not in LMFDB) 3.13.c_q_ai $12$ (not in LMFDB) 3.13.d_bd_cc $12$ (not in LMFDB) 3.13.e_w_bs $12$ (not in LMFDB) 3.13.f_bl_ec $12$ (not in LMFDB) 3.13.g_bg_ds $12$ (not in LMFDB) 3.13.j_cn_jy $12$ (not in LMFDB) 3.13.m_di_oi $12$ (not in LMFDB)