Properties

Label 5.3.al_cj_aio_wn_absr
Base Field $\F_{3}$
Dimension $5$
Ordinary No
$p$-rank $2$
Principally polarizable Yes
Contains a Jacobian No

Learn more about

Invariants

Base field:  $\F_{3}$
Dimension:  $5$
L-polynomial:  $( 1 - x + 3 x^{2} )^{2}( 1 - 3 x + 3 x^{2} )^{3}$
Frobenius angles:  $\pm0.166666666667$, $\pm0.166666666667$, $\pm0.166666666667$, $\pm0.406785250661$, $\pm0.406785250661$
Angle rank:  $1$ (numerical)

This isogeny class is not simple.

Newton polygon

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

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
$A(\F_{q^r})$ 9 77175 28449792 4238836875 902957021559 249811933593600 60247323228432069 13061567448051451875 2914370282453391369216 697768996307719253754375

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -7 11 44 95 263 872 2597 7031 19412 57371

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{3}$
The isogeny class factors as 1.3.ad 3 $\times$ 1.3.ab 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 $\F_{3^{6}}$ is 1.729.ak 2 $\times$ 1.729.cc 3 . The endomorphism algebra for each factor is:
All geometric endomorphisms are defined over $\F_{3^{6}}$.
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.aj_bp_aew_ll_avv$2$(not in LMFDB)
5.3.ah_z_aco_fx_all$2$(not in LMFDB)
5.3.af_n_as_j_j$2$(not in LMFDB)
5.3.ad_f_ag_j_aj$2$(not in LMFDB)
5.3.ab_b_ag_j_j$2$(not in LMFDB)
5.3.b_b_g_j_aj$2$(not in LMFDB)
5.3.d_f_g_j_j$2$(not in LMFDB)
5.3.f_n_s_j_aj$2$(not in LMFDB)
5.3.h_z_co_fx_ll$2$(not in LMFDB)
5.3.j_bp_ew_ll_vv$2$(not in LMFDB)
5.3.l_cj_io_wn_bsr$2$(not in LMFDB)
5.3.ai_z_ay_acl_ii$3$(not in LMFDB)
5.3.ai_bl_aeq_ll_awe$3$(not in LMFDB)
5.3.af_k_ad_abb_cu$3$(not in LMFDB)
5.3.af_w_acl_fx_alc$3$(not in LMFDB)
5.3.ac_af_s_j_acu$3$(not in LMFDB)
5.3.ac_e_a_aj_bk$3$(not in LMFDB)
5.3.ac_h_ag_j_a$3$(not in LMFDB)
5.3.ac_q_ay_dv_aee$3$(not in LMFDB)
5.3.b_ac_d_j_a$3$(not in LMFDB)
5.3.b_h_m_s_cc$3$(not in LMFDB)
5.3.b_k_p_bt_cu$3$(not in LMFDB)
5.3.e_b_am_j_cu$3$(not in LMFDB)
5.3.e_k_y_bt_cu$3$(not in LMFDB)
5.3.e_n_bk_dd_fo$3$(not in LMFDB)
5.3.h_w_bt_dd_fo$3$(not in LMFDB)
5.3.k_br_dy_fx_ii$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
5.3.aj_bp_aew_ll_avv$2$(not in LMFDB)
5.3.ah_z_aco_fx_all$2$(not in LMFDB)
5.3.af_n_as_j_j$2$(not in LMFDB)
5.3.ad_f_ag_j_aj$2$(not in LMFDB)
5.3.ab_b_ag_j_j$2$(not in LMFDB)
5.3.b_b_g_j_aj$2$(not in LMFDB)
5.3.d_f_g_j_j$2$(not in LMFDB)
5.3.f_n_s_j_aj$2$(not in LMFDB)
5.3.h_z_co_fx_ll$2$(not in LMFDB)
5.3.j_bp_ew_ll_vv$2$(not in LMFDB)
5.3.l_cj_io_wn_bsr$2$(not in LMFDB)
5.3.ai_z_ay_acl_ii$3$(not in LMFDB)
5.3.ai_bl_aeq_ll_awe$3$(not in LMFDB)
5.3.af_k_ad_abb_cu$3$(not in LMFDB)
5.3.af_w_acl_fx_alc$3$(not in LMFDB)
5.3.ac_af_s_j_acu$3$(not in LMFDB)
5.3.ac_e_a_aj_bk$3$(not in LMFDB)
5.3.ac_h_ag_j_a$3$(not in LMFDB)
5.3.ac_q_ay_dv_aee$3$(not in LMFDB)
5.3.b_ac_d_j_a$3$(not in LMFDB)
5.3.b_h_m_s_cc$3$(not in LMFDB)
5.3.b_k_p_bt_cu$3$(not in LMFDB)
5.3.e_b_am_j_cu$3$(not in LMFDB)
5.3.e_k_y_bt_cu$3$(not in LMFDB)
5.3.e_n_bk_dd_fo$3$(not in LMFDB)
5.3.h_w_bt_dd_fo$3$(not in LMFDB)
5.3.k_br_dy_fx_ii$3$(not in LMFDB)
5.3.aj_bf_abk_acl_jj$4$(not in LMFDB)
5.3.af_t_abw_eb_ahh$4$(not in LMFDB)
5.3.ad_af_y_j_adv$4$(not in LMFDB)
5.3.ad_b_g_ad_aj$4$(not in LMFDB)
5.3.ad_l_ay_cf_adv$4$(not in LMFDB)
5.3.ab_h_am_bh_abt$4$(not in LMFDB)
5.3.b_h_m_bh_bt$4$(not in LMFDB)
5.3.d_af_ay_j_dv$4$(not in LMFDB)
5.3.d_b_ag_ad_j$4$(not in LMFDB)
5.3.d_l_y_cf_dv$4$(not in LMFDB)
5.3.f_t_bw_eb_hh$4$(not in LMFDB)
5.3.j_bf_bk_acl_ajj$4$(not in LMFDB)
5.3.ak_br_ady_fx_aii$6$(not in LMFDB)
5.3.ah_w_abt_dd_afo$6$(not in LMFDB)
5.3.ag_x_aco_fx_alc$6$(not in LMFDB)
5.3.ae_b_m_j_acu$6$(not in LMFDB)
5.3.ae_k_ay_bt_acu$6$(not in LMFDB)
5.3.ae_n_abk_dd_afo$6$(not in LMFDB)
5.3.ad_o_abh_dd_afo$6$(not in LMFDB)
5.3.ab_ac_ad_j_a$6$(not in LMFDB)
5.3.ab_h_am_s_acc$6$(not in LMFDB)
5.3.ab_k_ap_bt_acu$6$(not in LMFDB)
5.3.a_f_a_j_a$6$(not in LMFDB)
5.3.a_o_a_dd_a$6$(not in LMFDB)
5.3.c_af_as_j_cu$6$(not in LMFDB)
5.3.c_e_a_aj_abk$6$(not in LMFDB)
5.3.c_h_g_j_a$6$(not in LMFDB)
5.3.c_q_y_dv_ee$6$(not in LMFDB)
5.3.d_o_bh_dd_fo$6$(not in LMFDB)
5.3.f_k_d_abb_acu$6$(not in LMFDB)
5.3.f_w_cl_fx_lc$6$(not in LMFDB)
5.3.g_x_co_fx_lc$6$(not in LMFDB)
5.3.i_z_y_acl_aii$6$(not in LMFDB)
5.3.i_bl_eq_ll_we$6$(not in LMFDB)
5.3.ac_h_ap_bb_acl$9$(not in LMFDB)
5.3.ac_h_d_aj_cl$9$(not in LMFDB)
5.3.b_ac_ag_a_s$9$(not in LMFDB)
5.3.b_ac_m_s_as$9$(not in LMFDB)
5.3.ag_n_ag_abb_cu$12$(not in LMFDB)
5.3.af_k_ad_abn_ee$12$(not in LMFDB)
5.3.ae_ac_y_ad_acu$12$(not in LMFDB)
5.3.ae_h_am_bh_acu$12$(not in LMFDB)
5.3.ad_ai_bh_p_afo$12$(not in LMFDB)
5.3.ad_c_d_ap_bk$12$(not in LMFDB)
5.3.ad_e_ad_aj_bk$12$(not in LMFDB)
5.3.ac_ai_y_p_aee$12$(not in LMFDB)
5.3.ac_b_g_ad_a$12$(not in LMFDB)
5.3.ac_e_a_av_bk$12$(not in LMFDB)
5.3.ac_n_as_cr_acu$12$(not in LMFDB)
5.3.ab_af_a_g_s$12$(not in LMFDB)
5.3.ab_ac_ad_ad_bk$12$(not in LMFDB)
5.3.ab_e_aj_p_abk$12$(not in LMFDB)
5.3.a_ai_a_p_a$12$(not in LMFDB)
5.3.a_af_a_j_a$12$(not in LMFDB)
5.3.a_b_a_ad_a$12$(not in LMFDB)
5.3.a_c_a_ap_a$12$(not in LMFDB)
5.3.a_e_a_aj_a$12$(not in LMFDB)
5.3.a_l_a_cf_a$12$(not in LMFDB)
5.3.b_af_a_g_as$12$(not in LMFDB)
5.3.b_ac_d_ad_abk$12$(not in LMFDB)
5.3.b_e_j_p_bk$12$(not in LMFDB)
5.3.c_ai_ay_p_ee$12$(not in LMFDB)
5.3.c_b_ag_ad_a$12$(not in LMFDB)
5.3.c_e_a_av_abk$12$(not in LMFDB)
5.3.c_n_s_cr_cu$12$(not in LMFDB)
5.3.d_ai_abh_p_fo$12$(not in LMFDB)
5.3.d_c_ad_ap_abk$12$(not in LMFDB)
5.3.d_e_d_aj_abk$12$(not in LMFDB)
5.3.e_ac_ay_ad_cu$12$(not in LMFDB)
5.3.e_h_m_bh_cu$12$(not in LMFDB)
5.3.f_k_d_abn_aee$12$(not in LMFDB)
5.3.g_n_g_abb_acu$12$(not in LMFDB)
5.3.ab_ac_am_s_s$18$(not in LMFDB)
5.3.ab_ac_g_a_as$18$(not in LMFDB)
5.3.a_f_aj_j_abt$18$(not in LMFDB)
5.3.a_f_j_j_bt$18$(not in LMFDB)
5.3.c_h_ad_aj_acl$18$(not in LMFDB)
5.3.c_h_p_bb_cl$18$(not in LMFDB)
5.3.af_q_abh_cf_adm$24$(not in LMFDB)
5.3.ae_e_a_v_acu$24$(not in LMFDB)
5.3.ad_ac_p_d_acc$24$(not in LMFDB)
5.3.ad_i_ap_bh_acc$24$(not in LMFDB)
5.3.ac_ac_m_d_abk$24$(not in LMFDB)
5.3.ac_k_am_bn_abk$24$(not in LMFDB)
5.3.ab_b_ag_m_as$24$(not in LMFDB)
5.3.ab_e_aj_v_as$24$(not in LMFDB)
5.3.a_ac_a_d_a$24$(not in LMFDB)
5.3.a_i_a_bh_a$24$(not in LMFDB)
5.3.b_b_g_m_s$24$(not in LMFDB)
5.3.b_e_j_v_s$24$(not in LMFDB)
5.3.c_ac_am_d_bk$24$(not in LMFDB)
5.3.c_k_m_bn_bk$24$(not in LMFDB)
5.3.d_ac_ap_d_cc$24$(not in LMFDB)
5.3.d_i_p_bh_cc$24$(not in LMFDB)
5.3.e_e_a_v_cu$24$(not in LMFDB)
5.3.f_q_bh_cf_dm$24$(not in LMFDB)
5.3.a_af_aj_j_bt$36$(not in LMFDB)
5.3.a_af_j_j_abt$36$(not in LMFDB)