Properties

Label 5.3.ao_dp_aou_bpx_adhe
Base Field $\F_{3}$
Dimension $5$
Ordinary No
$p$-rank $1$
Principally polarizable Yes
Contains a Jacobian No

Learn more about

Invariants

Base field:  $\F_{3}$
Dimension:  $5$
L-polynomial:  $( 1 - 2 x + 3 x^{2} )( 1 - 3 x + 3 x^{2} )^{4}$
Frobenius angles:  $\pm0.166666666667$, $\pm0.166666666667$, $\pm0.166666666667$, $\pm0.166666666667$, $\pm0.304086723985$
Angle rank:  $1$ (numerical)

This isogeny class is not simple.

Newton polygon

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

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
$A(\F_{q^r})$ 2 28812 23356928 6583196256 1305246476402 258416566861824 55714815313246742 12712681180316627328 2983587032589360587264 711977996323730431211532

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -10 0 38 132 350 900 2426 6852 19874 58560

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{3}$
The isogeny class factors as 1.3.ad 4 $\times$ 1.3.ac 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.abu $\times$ 1.729.cc 4 . 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.ak_bt_aeq_ir_aoo$2$(not in LMFDB)
5.3.ai_bb_abq_j_cc$2$(not in LMFDB)
5.3.ae_d_g_j_acc$2$(not in LMFDB)
5.3.ac_ad_m_j_acc$2$(not in LMFDB)
5.3.c_ad_am_j_cc$2$(not in LMFDB)
5.3.e_d_ag_j_cc$2$(not in LMFDB)
5.3.i_bb_bq_j_acc$2$(not in LMFDB)
5.3.k_bt_eq_ir_oo$2$(not in LMFDB)
5.3.o_dp_ou_bpx_dhe$2$(not in LMFDB)
5.3.al_ci_aif_vd_abpo$3$(not in LMFDB)
5.3.ai_bb_abq_j_cc$3$(not in LMFDB)
5.3.ai_bk_aek_kt_auu$3$(not in LMFDB)
5.3.af_m_ap_j_a$3$(not in LMFDB)
5.3.af_v_aci_fo_akk$3$(not in LMFDB)
5.3.ac_ad_m_j_acc$3$(not in LMFDB)
5.3.ac_g_ag_j_a$3$(not in LMFDB)
5.3.ac_p_ay_dm_aee$3$(not in LMFDB)
5.3.b_a_d_j_a$3$(not in LMFDB)
5.3.b_j_m_bk_cc$3$(not in LMFDB)
5.3.e_d_ag_j_cc$3$(not in LMFDB)
5.3.e_m_be_cl_ee$3$(not in LMFDB)
5.3.h_y_cf_en_ii$3$(not in LMFDB)
5.3.k_bt_eq_ir_oo$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
5.3.ak_bt_aeq_ir_aoo$2$(not in LMFDB)
5.3.ai_bb_abq_j_cc$2$(not in LMFDB)
5.3.ae_d_g_j_acc$2$(not in LMFDB)
5.3.ac_ad_m_j_acc$2$(not in LMFDB)
5.3.c_ad_am_j_cc$2$(not in LMFDB)
5.3.e_d_ag_j_cc$2$(not in LMFDB)
5.3.i_bb_bq_j_acc$2$(not in LMFDB)
5.3.k_bt_eq_ir_oo$2$(not in LMFDB)
5.3.o_dp_ou_bpx_dhe$2$(not in LMFDB)
5.3.al_ci_aif_vd_abpo$3$(not in LMFDB)
5.3.ai_bb_abq_j_cc$3$(not in LMFDB)
5.3.ai_bk_aek_kt_auu$3$(not in LMFDB)
5.3.af_m_ap_j_a$3$(not in LMFDB)
5.3.af_v_aci_fo_akk$3$(not in LMFDB)
5.3.ac_ad_m_j_acc$3$(not in LMFDB)
5.3.ac_g_ag_j_a$3$(not in LMFDB)
5.3.ac_p_ay_dm_aee$3$(not in LMFDB)
5.3.b_a_d_j_a$3$(not in LMFDB)
5.3.b_j_m_bk_cc$3$(not in LMFDB)
5.3.e_d_ag_j_cc$3$(not in LMFDB)
5.3.e_m_be_cl_ee$3$(not in LMFDB)
5.3.h_y_cf_en_ii$3$(not in LMFDB)
5.3.k_bt_eq_ir_oo$3$(not in LMFDB)
5.3.ai_bh_adm_hh_ane$4$(not in LMFDB)
5.3.ae_j_as_bt_adm$4$(not in LMFDB)
5.3.ac_d_a_j_as$4$(not in LMFDB)
5.3.ac_j_am_bt_acc$4$(not in LMFDB)
5.3.c_d_a_j_s$4$(not in LMFDB)
5.3.c_j_m_bt_cc$4$(not in LMFDB)
5.3.e_j_s_bt_dm$4$(not in LMFDB)
5.3.i_bh_dm_hh_ne$4$(not in LMFDB)
5.3.b_d_g_j_bk$5$(not in LMFDB)
5.3.ah_y_acf_en_aii$6$(not in LMFDB)
5.3.ae_m_abe_cl_aee$6$(not in LMFDB)
5.3.ab_a_ad_j_a$6$(not in LMFDB)
5.3.ab_j_am_bk_acc$6$(not in LMFDB)
5.3.c_g_g_j_a$6$(not in LMFDB)
5.3.c_p_y_dm_ee$6$(not in LMFDB)
5.3.f_m_p_j_a$6$(not in LMFDB)
5.3.f_v_ci_fo_kk$6$(not in LMFDB)
5.3.i_bk_ek_kt_uu$6$(not in LMFDB)
5.3.l_ci_if_vd_bpo$6$(not in LMFDB)
5.3.ac_d_a_aj_s$8$(not in LMFDB)
5.3.c_d_a_aj_as$8$(not in LMFDB)
5.3.af_m_ay_cc_aee$9$(not in LMFDB)
5.3.af_m_ag_abk_ee$9$(not in LMFDB)
5.3.ac_g_ap_bb_acc$9$(not in LMFDB)
5.3.ac_g_d_aj_cc$9$(not in LMFDB)
5.3.b_a_ag_a_a$9$(not in LMFDB)
5.3.b_a_m_s_a$9$(not in LMFDB)
5.3.af_p_abe_bt_acu$10$(not in LMFDB)
5.3.ab_d_ag_j_abk$10$(not in LMFDB)
5.3.f_p_be_bt_cu$10$(not in LMFDB)
5.3.ai_y_as_add_js$12$(not in LMFDB)
5.3.af_j_a_abk_dm$12$(not in LMFDB)
5.3.af_s_abt_dv_agy$12$(not in LMFDB)
5.3.ae_a_s_aj_abk$12$(not in LMFDB)
5.3.ac_aj_y_s_aee$12$(not in LMFDB)
5.3.ac_ag_s_j_acu$12$(not in LMFDB)
5.3.ac_a_g_aj_a$12$(not in LMFDB)
5.3.ac_d_a_as_bk$12$(not in LMFDB)
5.3.ac_m_as_cl_acu$12$(not in LMFDB)
5.3.ab_ad_a_a_s$12$(not in LMFDB)
5.3.ab_g_aj_bb_abk$12$(not in LMFDB)
5.3.b_ad_a_a_as$12$(not in LMFDB)
5.3.b_g_j_bb_bk$12$(not in LMFDB)
5.3.c_aj_ay_s_ee$12$(not in LMFDB)
5.3.c_ag_as_j_cu$12$(not in LMFDB)
5.3.c_a_ag_aj_a$12$(not in LMFDB)
5.3.c_d_a_as_abk$12$(not in LMFDB)
5.3.c_m_s_cl_cu$12$(not in LMFDB)
5.3.e_a_as_aj_bk$12$(not in LMFDB)
5.3.f_j_a_abk_adm$12$(not in LMFDB)
5.3.f_s_bt_dv_gy$12$(not in LMFDB)
5.3.i_y_s_add_ajs$12$(not in LMFDB)
5.3.af_p_abe_bt_acu$15$(not in LMFDB)
5.3.ac_a_g_a_as$15$(not in LMFDB)
5.3.ab_a_am_s_a$18$(not in LMFDB)
5.3.ab_a_g_a_a$18$(not in LMFDB)
5.3.c_g_ad_aj_acc$18$(not in LMFDB)
5.3.c_g_p_bb_cc$18$(not in LMFDB)
5.3.f_m_g_abk_aee$18$(not in LMFDB)
5.3.f_m_y_cc_ee$18$(not in LMFDB)
5.3.ai_be_aco_dv_afo$24$(not in LMFDB)
5.3.af_p_abe_cc_adm$24$(not in LMFDB)
5.3.ae_g_ag_bb_acu$24$(not in LMFDB)
5.3.ac_ad_m_a_abk$24$(not in LMFDB)
5.3.ac_a_g_j_abk$24$(not in LMFDB)
5.3.ac_d_a_s_abk$24$(not in LMFDB)
5.3.ac_g_ag_bb_abk$24$(not in LMFDB)
5.3.ac_j_am_bk_abk$24$(not in LMFDB)
5.3.ab_d_ag_s_as$24$(not in LMFDB)
5.3.b_d_g_s_s$24$(not in LMFDB)
5.3.c_ad_am_a_bk$24$(not in LMFDB)
5.3.c_a_ag_j_bk$24$(not in LMFDB)
5.3.c_d_a_s_bk$24$(not in LMFDB)
5.3.c_g_g_bb_bk$24$(not in LMFDB)
5.3.c_j_m_bk_bk$24$(not in LMFDB)
5.3.e_g_g_bb_cu$24$(not in LMFDB)
5.3.f_p_be_cc_dm$24$(not in LMFDB)
5.3.i_be_co_dv_fo$24$(not in LMFDB)
5.3.c_a_ag_a_s$30$(not in LMFDB)
5.3.ac_d_a_a_a$48$(not in LMFDB)
5.3.c_d_a_a_a$48$(not in LMFDB)
5.3.ac_g_ag_s_as$60$(not in LMFDB)
5.3.c_g_g_s_s$60$(not in LMFDB)