Properties

Label 5.3.al_ch_aia_us_abow
Base Field $\F_{3}$
Dimension $5$
Ordinary No
$p$-rank $4$
Principally polarizable Yes
Contains a Jacobian No

Learn more about

Invariants

Base field:  $\F_{3}$
Dimension:  $5$
L-polynomial:  $( 1 - 3 x + 3 x^{2} )( 1 - 4 x + 8 x^{2} - 12 x^{3} + 9 x^{4} )^{2}$
Frobenius angles:  $\pm0.0540867239847$, $\pm0.0540867239847$, $\pm0.166666666667$, $\pm0.445913276015$, $\pm0.445913276015$
Angle rank:  $1$ (numerical)

This isogeny class is not simple.

Newton polygon

$p$-rank:  $4$
Slopes:  $[0, 0, 0, 0, 1/2, 1/2, 1, 1, 1, 1]$

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
$A(\F_{q^r})$ 4 32368 10972528 1945705216 658181907004 221974241440000 54436404955943476 12063819633480695808 2868089541454266945424 715002677300852642155888

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -7 7 20 35 183 784 2373 6507 19100 58807

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{3}$
The isogeny class factors as 1.3.ad $\times$ 2.3.ae_i 2 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 $\overline{\F}_{3}$
The base change of $A$ to $\F_{3^{12}}$ is 1.531441.acec $\times$ 1.531441.zi 4 . The endomorphism algebra for each factor is:
All geometric endomorphisms are defined over $\F_{3^{12}}$.
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
5.3.af_l_aq_k_g$2$(not in LMFDB)
5.3.ad_d_a_ao_bq$2$(not in LMFDB)
5.3.d_d_a_ao_abq$2$(not in LMFDB)
5.3.f_l_q_k_ag$2$(not in LMFDB)
5.3.l_ch_ia_us_bow$2$(not in LMFDB)
5.3.ai_bj_aei_ko_aui$3$(not in LMFDB)
5.3.af_l_aq_k_g$3$(not in LMFDB)
5.3.b_ab_ae_h_bb$3$(not in LMFDB)
5.3.e_l_u_bf_bw$3$(not in LMFDB)
5.3.h_x_bs_cd_cr$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
5.3.af_l_aq_k_g$2$(not in LMFDB)
5.3.ad_d_a_ao_bq$2$(not in LMFDB)
5.3.d_d_a_ao_abq$2$(not in LMFDB)
5.3.f_l_q_k_ag$2$(not in LMFDB)
5.3.l_ch_ia_us_bow$2$(not in LMFDB)
5.3.ai_bj_aei_ko_aui$3$(not in LMFDB)
5.3.af_l_aq_k_g$3$(not in LMFDB)
5.3.b_ab_ae_h_bb$3$(not in LMFDB)
5.3.e_l_u_bf_bw$3$(not in LMFDB)
5.3.h_x_bs_cd_cr$3$(not in LMFDB)
5.3.ah_x_abs_cd_acr$6$(not in LMFDB)
5.3.ae_l_au_bf_abw$6$(not in LMFDB)
5.3.ab_ab_e_h_abb$6$(not in LMFDB)
5.3.a_d_a_ao_a$6$(not in LMFDB)
5.3.i_bj_ei_ko_ui$6$(not in LMFDB)
5.3.al_cj_aio_wm_abso$8$(not in LMFDB)
5.3.al_cl_ajc_yk_abws$8$(not in LMFDB)
5.3.ah_v_abi_bg_abe$8$(not in LMFDB)
5.3.ah_x_abo_bi_as$8$(not in LMFDB)
5.3.ah_z_ack_eu_aio$8$(not in LMFDB)
5.3.ah_bb_acq_fe_aja$8$(not in LMFDB)
5.3.af_n_as_i_g$8$(not in LMFDB)
5.3.af_p_au_k_s$8$(not in LMFDB)
5.3.ad_ab_m_k_aco$8$(not in LMFDB)
5.3.ad_d_a_o_abq$8$(not in LMFDB)
5.3.ad_f_ao_bg_acc$8$(not in LMFDB)
5.3.ad_f_c_aq_bq$8$(not in LMFDB)
5.3.ad_h_am_bi_aco$8$(not in LMFDB)
5.3.ab_ad_c_i_as$8$(not in LMFDB)
5.3.ab_ab_i_k_abe$8$(not in LMFDB)
5.3.ab_b_ac_e_as$8$(not in LMFDB)
5.3.ab_d_e_o_ag$8$(not in LMFDB)
5.3.b_ad_ac_i_s$8$(not in LMFDB)
5.3.b_ab_ai_k_be$8$(not in LMFDB)
5.3.b_b_c_e_s$8$(not in LMFDB)
5.3.b_d_ae_o_g$8$(not in LMFDB)
5.3.d_ab_am_k_co$8$(not in LMFDB)
5.3.d_d_a_o_bq$8$(not in LMFDB)
5.3.d_f_ac_aq_abq$8$(not in LMFDB)
5.3.d_f_o_bg_cc$8$(not in LMFDB)
5.3.d_h_m_bi_co$8$(not in LMFDB)
5.3.f_n_s_i_ag$8$(not in LMFDB)
5.3.f_p_u_k_as$8$(not in LMFDB)
5.3.h_v_bi_bg_be$8$(not in LMFDB)
5.3.h_x_bo_bi_s$8$(not in LMFDB)
5.3.h_z_ck_eu_io$8$(not in LMFDB)
5.3.h_bb_cq_fe_ja$8$(not in LMFDB)
5.3.l_cj_io_wm_bso$8$(not in LMFDB)
5.3.l_cl_jc_yk_bws$8$(not in LMFDB)
5.3.ah_x_abs_cd_acr$12$(not in LMFDB)
5.3.ad_af_y_i_ads$16$(not in LMFDB)
5.3.ad_l_ay_ce_ads$16$(not in LMFDB)
5.3.d_af_ay_i_ds$16$(not in LMFDB)
5.3.d_l_y_ce_ds$16$(not in LMFDB)
5.3.aj_bm_aed_jf_ari$24$(not in LMFDB)
5.3.aj_bo_aen_jz_asm$24$(not in LMFDB)
5.3.ai_bl_aeq_lk_awe$24$(not in LMFDB)
5.3.ai_bn_aey_mk_aya$24$(not in LMFDB)
5.3.ah_v_abu_ef_air$24$(not in LMFDB)
5.3.ag_u_ace_ev_aiu$24$(not in LMFDB)
5.3.ag_w_aci_fd_ajs$24$(not in LMFDB)
5.3.af_i_af_t_aci$24$(not in LMFDB)
5.3.af_k_ad_abl_dy$24$(not in LMFDB)
5.3.af_m_az_ch_aeq$24$(not in LMFDB)
5.3.af_m_af_abp_eq$24$(not in LMFDB)
5.3.ae_j_abc_cj_ads$24$(not in LMFDB)
5.3.ae_j_aq_u_ay$24$(not in LMFDB)
5.3.ae_l_aq_w_ay$24$(not in LMFDB)
5.3.ae_n_abg_cm_aeq$24$(not in LMFDB)
5.3.ae_p_abg_cw_aeq$24$(not in LMFDB)
5.3.ad_b_g_al_p$24$(not in LMFDB)
5.3.ad_c_af_l_ag$24$(not in LMFDB)
5.3.ad_e_ad_h_ay$24$(not in LMFDB)
5.3.ad_f_ag_b_p$24$(not in LMFDB)
5.3.ac_c_ai_n_am$24$(not in LMFDB)
5.3.ac_e_a_at_bk$24$(not in LMFDB)
5.3.ac_g_aq_bd_aci$24$(not in LMFDB)
5.3.ac_g_e_al_ci$24$(not in LMFDB)
5.3.ab_ae_l_h_abk$24$(not in LMFDB)
5.3.ab_ad_ak_n_bh$24$(not in LMFDB)
5.3.ab_ac_ad_ab_be$24$(not in LMFDB)
5.3.ab_a_an_t_a$24$(not in LMFDB)
5.3.ab_a_h_ab_a$24$(not in LMFDB)
5.3.a_ab_a_k_a$24$(not in LMFDB)
5.3.a_b_a_al_a$24$(not in LMFDB)
5.3.a_d_a_o_a$24$(not in LMFDB)
5.3.a_f_ai_i_abw$24$(not in LMFDB)
5.3.a_f_a_b_a$24$(not in LMFDB)
5.3.a_f_i_i_bw$24$(not in LMFDB)
5.3.a_h_a_bi_a$24$(not in LMFDB)
5.3.b_ae_al_h_bk$24$(not in LMFDB)
5.3.b_ad_k_n_abh$24$(not in LMFDB)
5.3.b_ac_d_ab_abe$24$(not in LMFDB)
5.3.b_a_ah_ab_a$24$(not in LMFDB)
5.3.b_a_n_t_a$24$(not in LMFDB)
5.3.c_c_i_n_m$24$(not in LMFDB)
5.3.c_e_a_at_abk$24$(not in LMFDB)
5.3.c_g_ae_al_aci$24$(not in LMFDB)
5.3.c_g_q_bd_ci$24$(not in LMFDB)
5.3.d_b_ag_al_ap$24$(not in LMFDB)
5.3.d_c_f_l_g$24$(not in LMFDB)
5.3.d_e_d_h_y$24$(not in LMFDB)
5.3.d_f_g_b_ap$24$(not in LMFDB)
5.3.e_j_q_u_y$24$(not in LMFDB)
5.3.e_j_bc_cj_ds$24$(not in LMFDB)
5.3.e_l_q_w_y$24$(not in LMFDB)
5.3.e_n_bg_cm_eq$24$(not in LMFDB)
5.3.e_p_bg_cw_eq$24$(not in LMFDB)
5.3.f_i_f_t_ci$24$(not in LMFDB)
5.3.f_k_d_abl_ady$24$(not in LMFDB)
5.3.f_m_f_abp_aeq$24$(not in LMFDB)
5.3.f_m_z_ch_eq$24$(not in LMFDB)
5.3.g_u_ce_ev_iu$24$(not in LMFDB)
5.3.g_w_ci_fd_js$24$(not in LMFDB)
5.3.h_v_bu_ef_ir$24$(not in LMFDB)
5.3.i_bl_eq_lk_we$24$(not in LMFDB)
5.3.i_bn_ey_mk_ya$24$(not in LMFDB)
5.3.j_bm_ed_jf_ri$24$(not in LMFDB)
5.3.j_bo_en_jz_sm$24$(not in LMFDB)
5.3.af_k_af_au_cf$40$(not in LMFDB)
5.3.ab_ac_ab_e_j$40$(not in LMFDB)
5.3.b_ac_b_e_aj$40$(not in LMFDB)
5.3.f_k_f_au_acf$40$(not in LMFDB)
5.3.a_af_a_i_a$48$(not in LMFDB)
5.3.a_l_a_ce_a$48$(not in LMFDB)
5.3.ac_e_ac_ai_y$120$(not in LMFDB)
5.3.c_e_c_ai_ay$120$(not in LMFDB)