# Properties

 Label 3.13.aq_eu_avu 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: $( 1 - 6 x + 13 x^{2} )( 1 - 5 x + 13 x^{2} )^{2}$ Frobenius angles: $\pm0.187167041811$, $\pm0.256122854178$, $\pm0.256122854178$ 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 $A(\F_{q^r})$ 648 4678560 11398713984 24052383388800 51565503209383368 112526703776073646080 247000310295547016257704 542725971452014256712000000 1192493984943955799137953449088 2619988058269821139027985850544800

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ -2 162 2356 29474 374038 4829868 62732206 815618306 10604149828 137858092722

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{13}$
 The isogeny class factors as 1.13.ag $\times$ 1.13.af 2 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 : $$\Q(\sqrt{-1})$$. 1.13.af 2 : $\mathrm{M}_{2}($$$\Q(\sqrt{-3})$$$)$
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.ag_o_ag $2$ (not in LMFDB) 3.13.ae_e_bu $2$ (not in LMFDB) 3.13.e_e_abu $2$ (not in LMFDB) 3.13.g_o_g $2$ (not in LMFDB) 3.13.q_eu_vu $2$ (not in LMFDB) 3.13.an_dn_api $3$ (not in LMFDB) 3.13.ak_cp_aky $3$ (not in LMFDB) 3.13.ae_ai_ec $3$ (not in LMFDB) 3.13.ab_af_cg $3$ (not in LMFDB) 3.13.i_e_adi $3$ (not in LMFDB)
Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 3.13.ag_o_ag $2$ (not in LMFDB) 3.13.ae_e_bu $2$ (not in LMFDB) 3.13.e_e_abu $2$ (not in LMFDB) 3.13.g_o_g $2$ (not in LMFDB) 3.13.q_eu_vu $2$ (not in LMFDB) 3.13.an_dn_api $3$ (not in LMFDB) 3.13.ak_cp_aky $3$ (not in LMFDB) 3.13.ae_ai_ec $3$ (not in LMFDB) 3.13.ab_af_cg $3$ (not in LMFDB) 3.13.i_e_adi $3$ (not in LMFDB) 3.13.ao_ea_arw $4$ (not in LMFDB) 3.13.ag_m_g $4$ (not in LMFDB) 3.13.ag_y_ace $4$ (not in LMFDB) 3.13.ae_m_e $4$ (not in LMFDB) 3.13.ae_o_ae $4$ (not in LMFDB) 3.13.e_m_ae $4$ (not in LMFDB) 3.13.e_o_e $4$ (not in LMFDB) 3.13.g_m_ag $4$ (not in LMFDB) 3.13.g_y_ce $4$ (not in LMFDB) 3.13.o_ea_rw $4$ (not in LMFDB) 3.13.au_gq_abfi $6$ (not in LMFDB) 3.13.as_fq_abac $6$ (not in LMFDB) 3.13.ap_ed_asg $6$ (not in LMFDB) 3.13.al_cd_ahu $6$ (not in LMFDB) 3.13.aj_bv_ags $6$ (not in LMFDB) 3.13.ai_e_di $6$ (not in LMFDB) 3.13.ai_q_c $6$ (not in LMFDB) 3.13.ag_ak_fi $6$ (not in LMFDB) 3.13.ag_c_cc $6$ (not in LMFDB) 3.13.ag_bj_afc $6$ (not in LMFDB) 3.13.ad_ab_g $6$ (not in LMFDB) 3.13.ad_l_as $6$ (not in LMFDB) 3.13.ac_t_acy $6$ (not in LMFDB) 3.13.ab_h_bi $6$ (not in LMFDB) 3.13.b_af_acg $6$ (not in LMFDB) 3.13.b_h_abi $6$ (not in LMFDB) 3.13.c_t_cy $6$ (not in LMFDB) 3.13.d_ab_ag $6$ (not in LMFDB) 3.13.d_l_s $6$ (not in LMFDB) 3.13.e_ai_aec $6$ (not in LMFDB) 3.13.g_ak_afi $6$ (not in LMFDB) 3.13.g_c_acc $6$ (not in LMFDB) 3.13.g_bj_fc $6$ (not in LMFDB) 3.13.i_q_ac $6$ (not in LMFDB) 3.13.j_bv_gs $6$ (not in LMFDB) 3.13.k_cp_ky $6$ (not in LMFDB) 3.13.l_cd_hu $6$ (not in LMFDB) 3.13.n_dn_pi $6$ (not in LMFDB) 3.13.p_ed_sg $6$ (not in LMFDB) 3.13.s_fq_bac $6$ (not in LMFDB) 3.13.u_gq_bfi $6$ (not in LMFDB) 3.13.as_fo_azo $12$ (not in LMFDB) 3.13.aq_es_avk $12$ (not in LMFDB) 3.13.an_dl_ape $12$ (not in LMFDB) 3.13.al_cz_amo $12$ (not in LMFDB) 3.13.ak_bg_acm $12$ (not in LMFDB) 3.13.aj_bt_agw $12$ (not in LMFDB) 3.13.ai_ba_acq $12$ (not in LMFDB) 3.13.ai_ch_aiq $12$ (not in LMFDB) 3.13.ah_bp_afm $12$ (not in LMFDB) 3.13.ag_aj_fc $12$ (not in LMFDB) 3.13.ag_m_aq $12$ (not in LMFDB) 3.13.ag_bk_afi $12$ (not in LMFDB) 3.13.af_r_acw $12$ (not in LMFDB) 3.13.ae_ak_do $12$ (not in LMFDB) 3.13.ae_aj_dk $12$ (not in LMFDB) 3.13.ae_bj_adk $12$ (not in LMFDB) 3.13.ae_bk_ado $12$ (not in LMFDB) 3.13.ad_v_abm $12$ (not in LMFDB) 3.13.ac_ae_dk $12$ (not in LMFDB) 3.13.ab_f_ade $12$ (not in LMFDB) 3.13.ab_r_o $12$ (not in LMFDB) 3.13.a_bb_aq $12$ (not in LMFDB) 3.13.a_bb_q $12$ (not in LMFDB) 3.13.b_f_de $12$ (not in LMFDB) 3.13.b_r_ao $12$ (not in LMFDB) 3.13.c_ae_adk $12$ (not in LMFDB) 3.13.d_v_bm $12$ (not in LMFDB) 3.13.e_ak_ado $12$ (not in LMFDB) 3.13.e_aj_adk $12$ (not in LMFDB) 3.13.e_bj_dk $12$ (not in LMFDB) 3.13.e_bk_do $12$ (not in LMFDB) 3.13.f_r_cw $12$ (not in LMFDB) 3.13.g_aj_afc $12$ (not in LMFDB) 3.13.g_m_q $12$ (not in LMFDB) 3.13.g_bk_fi $12$ (not in LMFDB) 3.13.h_bp_fm $12$ (not in LMFDB) 3.13.i_ba_cq $12$ (not in LMFDB) 3.13.i_ch_iq $12$ (not in LMFDB) 3.13.j_bt_gw $12$ (not in LMFDB) 3.13.k_bg_cm $12$ (not in LMFDB) 3.13.l_cz_mo $12$ (not in LMFDB) 3.13.n_dl_pe $12$ (not in LMFDB) 3.13.q_es_vk $12$ (not in LMFDB) 3.13.s_fo_zo $12$ (not in LMFDB)