Properties

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

Learn more about

Invariants

Base field:  $\F_{13}$
Dimension:  $3$
L-polynomial:  $( 1 - 7 x + 13 x^{2} )( 1 - 6 x + 13 x^{2} )( 1 - 4 x + 13 x^{2} )$
Frobenius angles:  $\pm0.0772104791556$, $\pm0.187167041811$, $\pm0.312832958189$
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.

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 560 4233600 10798833920 23532042240000 51258148307970800 112443608063027404800 247055866870251819395120 542815143389447140638720000 1192553296286215309816730420480 2620006291306630482093779865840000

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -3 147 2238 28847 371817 4826304 62746317 815752319 10604677254 137859052107

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{13}$
The isogeny class factors as 1.13.ah $\times$ 1.13.ag $\times$ 1.13.ae and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is:
Endomorphism algebra over $\overline{\F}_{13}$
The base change of $A$ to $\F_{13^{4}}$ is 1.28561.ahj $\times$ 1.28561.je 2 . The endomorphism algebra for each factor is:
All geometric endomorphisms are defined over $\F_{13^{4}}$.
Remainder of endomorphism lattice by field

Base change

This is a primitive isogeny class.

Twists

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