Properties

Label 5.3.ak_by_agm_qh_abfw
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:  $( 1 + 3 x^{2} )( 1 - 3 x + 3 x^{2} )^{2}( 1 - 4 x + 8 x^{2} - 12 x^{3} + 9 x^{4} )$
Frobenius angles:  $\pm0.0540867239847$, $\pm0.166666666667$, $\pm0.166666666667$, $\pm0.445913276015$, $\pm0.5$
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
$A(\F_{q^r})$ 8 53312 13741952 2450646016 883113924328 256413830758400 55175182657623064 12035628397913702400 2911251624101322728576 717921606084570114339392

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -6 10 24 54 254 892 2402 6494 19392 59050

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{3}$
The isogeny class factors as 1.3.ad 2 $\times$ 1.3.a $\times$ 2.3.ae_i 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 3 $\times$ 1.531441.zi 2 . 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.ae_i_am_j_a$2$(not in LMFDB)
5.3.ac_c_a_aj_bk$2$(not in LMFDB)
5.3.c_c_a_aj_abk$2$(not in LMFDB)
5.3.e_i_m_j_a$2$(not in LMFDB)
5.3.k_by_gm_qh_bfw$2$(not in LMFDB)
5.3.an_dc_alx_bgf_acmk$3$(not in LMFDB)
5.3.ah_u_abb_j_s$3$(not in LMFDB)
5.3.ah_bd_adm_ii_apy$3$(not in LMFDB)
5.3.ae_r_abw_ee_aii$3$(not in LMFDB)
5.3.ab_ae_d_j_as$3$(not in LMFDB)
5.3.ab_f_ag_a_as$3$(not in LMFDB)
5.3.f_i_ad_abb_acc$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
5.3.ae_i_am_j_a$2$(not in LMFDB)
5.3.ac_c_a_aj_bk$2$(not in LMFDB)
5.3.c_c_a_aj_abk$2$(not in LMFDB)
5.3.e_i_m_j_a$2$(not in LMFDB)
5.3.k_by_gm_qh_bfw$2$(not in LMFDB)
5.3.an_dc_alx_bgf_acmk$3$(not in LMFDB)
5.3.ah_u_abb_j_s$3$(not in LMFDB)
5.3.ah_bd_adm_ii_apy$3$(not in LMFDB)
5.3.ae_r_abw_ee_aii$3$(not in LMFDB)
5.3.ab_ae_d_j_as$3$(not in LMFDB)
5.3.ab_f_ag_a_as$3$(not in LMFDB)
5.3.f_i_ad_abb_acc$3$(not in LMFDB)
5.3.ae_o_abk_cx_afo$4$(not in LMFDB)
5.3.e_o_bk_cx_fo$4$(not in LMFDB)
5.3.af_i_d_abb_cc$6$(not in LMFDB)
5.3.b_ae_ad_j_s$6$(not in LMFDB)
5.3.b_f_g_a_s$6$(not in LMFDB)
5.3.e_r_bw_ee_ii$6$(not in LMFDB)
5.3.h_u_bb_j_as$6$(not in LMFDB)
5.3.h_bd_dm_ii_py$6$(not in LMFDB)
5.3.n_dc_lx_bgf_cmk$6$(not in LMFDB)
5.3.ak_ca_agy_rr_abiq$8$(not in LMFDB)
5.3.ag_q_ay_bb_abk$8$(not in LMFDB)
5.3.ag_u_abw_dv_agy$8$(not in LMFDB)
5.3.ae_k_am_j_a$8$(not in LMFDB)
5.3.ae_q_abk_dj_afo$8$(not in LMFDB)
5.3.ac_e_am_bb_abk$8$(not in LMFDB)
5.3.a_ac_a_j_a$8$(not in LMFDB)
5.3.a_c_a_j_a$8$(not in LMFDB)
5.3.a_e_a_p_a$8$(not in LMFDB)
5.3.a_i_a_bn_a$8$(not in LMFDB)
5.3.c_e_m_bb_bk$8$(not in LMFDB)
5.3.e_k_m_j_a$8$(not in LMFDB)
5.3.e_q_bk_dj_fo$8$(not in LMFDB)
5.3.g_q_y_bb_bk$8$(not in LMFDB)
5.3.g_u_bw_dv_gy$8$(not in LMFDB)
5.3.k_ca_gy_rr_biq$8$(not in LMFDB)
5.3.ae_i_av_bt_acu$9$(not in LMFDB)
5.3.ae_i_ad_abb_cu$9$(not in LMFDB)
5.3.ah_r_ag_aci_gg$12$(not in LMFDB)
5.3.ah_ba_acr_fr_akk$12$(not in LMFDB)
5.3.ae_f_a_ay_cu$12$(not in LMFDB)
5.3.ab_ah_g_m_as$12$(not in LMFDB)
5.3.ab_c_ad_d_as$12$(not in LMFDB)
5.3.b_ah_ag_m_s$12$(not in LMFDB)
5.3.b_c_d_d_s$12$(not in LMFDB)
5.3.e_f_a_ay_acu$12$(not in LMFDB)
5.3.h_r_g_aci_agg$12$(not in LMFDB)
5.3.h_ba_cr_fr_kk$12$(not in LMFDB)
5.3.e_i_d_abb_acu$18$(not in LMFDB)
5.3.e_i_v_bt_cu$18$(not in LMFDB)
5.3.an_de_amp_biz_acsq$24$(not in LMFDB)
5.3.al_cd_agm_of_azz$24$(not in LMFDB)
5.3.aj_bi_acl_bt_a$24$(not in LMFDB)
5.3.aj_bm_adv_hh_amm$24$(not in LMFDB)
5.3.ai_bf_adg_hh_anw$24$(not in LMFDB)
5.3.ah_t_am_aco_hq$24$(not in LMFDB)
5.3.ah_t_am_acl_hh$24$(not in LMFDB)
5.3.ah_w_abh_j_bk$24$(not in LMFDB)
5.3.ah_x_abw_da_aew$24$(not in LMFDB)
5.3.ah_z_acc_dg_aew$24$(not in LMFDB)
5.3.ah_bc_acx_gd_alc$24$(not in LMFDB)
5.3.ah_bf_ads_ja_ari$24$(not in LMFDB)
5.3.af_e_p_av_a$24$(not in LMFDB)
5.3.af_h_a_j_abt$24$(not in LMFDB)
5.3.af_k_ap_bn_adm$24$(not in LMFDB)
5.3.af_k_ap_bt_aee$24$(not in LMFDB)
5.3.af_n_abe_cr_aff$24$(not in LMFDB)
5.3.af_q_abt_dv_agy$24$(not in LMFDB)
5.3.ae_h_a_abe_cu$24$(not in LMFDB)
5.3.ae_h_a_abb_cu$24$(not in LMFDB)
5.3.ae_l_ay_bq_acu$24$(not in LMFDB)
5.3.ae_n_ay_bw_acu$24$(not in LMFDB)
5.3.ae_t_abw_ew_aii$24$(not in LMFDB)
5.3.ad_af_y_g_adm$24$(not in LMFDB)
5.3.ad_ac_p_j_acu$24$(not in LMFDB)
5.3.ad_ab_m_ag_as$24$(not in LMFDB)
5.3.ad_b_g_m_acc$24$(not in LMFDB)
5.3.ad_c_d_j_abk$24$(not in LMFDB)
5.3.ad_e_ad_p_abk$24$(not in LMFDB)
5.3.ad_f_ag_y_acc$24$(not in LMFDB)
5.3.ad_h_am_s_as$24$(not in LMFDB)
5.3.ad_i_ap_bn_acu$24$(not in LMFDB)
5.3.ad_l_ay_cc_adm$24$(not in LMFDB)
5.3.ac_ac_a_ad_bk$24$(not in LMFDB)
5.3.ac_b_ag_j_a$24$(not in LMFDB)
5.3.ac_e_am_v_abk$24$(not in LMFDB)
5.3.ac_h_as_bh_acu$24$(not in LMFDB)
5.3.ac_k_ay_bt_aee$24$(not in LMFDB)
5.3.ab_ai_p_p_acu$24$(not in LMFDB)
5.3.ab_af_m_g_acc$24$(not in LMFDB)
5.3.ab_af_m_j_abt$24$(not in LMFDB)
5.3.ab_ac_j_d_as$24$(not in LMFDB)
5.3.ab_ac_j_j_abk$24$(not in LMFDB)
5.3.ab_ab_a_g_as$24$(not in LMFDB)
5.3.ab_b_g_ad_j$24$(not in LMFDB)
5.3.ab_b_g_m_as$24$(not in LMFDB)
5.3.ab_e_d_aj_bk$24$(not in LMFDB)
5.3.ab_e_d_p_a$24$(not in LMFDB)
5.3.ab_h_a_s_s$24$(not in LMFDB)
5.3.a_af_a_g_a$24$(not in LMFDB)
5.3.a_ab_a_ag_a$24$(not in LMFDB)
5.3.a_b_a_m_a$24$(not in LMFDB)
5.3.a_f_a_y_a$24$(not in LMFDB)
5.3.a_h_a_s_a$24$(not in LMFDB)
5.3.a_l_a_cc_a$24$(not in LMFDB)
5.3.b_ai_ap_p_cu$24$(not in LMFDB)
5.3.b_af_am_g_cc$24$(not in LMFDB)
5.3.b_af_am_j_bt$24$(not in LMFDB)
5.3.b_ac_aj_d_s$24$(not in LMFDB)
5.3.b_ac_aj_j_bk$24$(not in LMFDB)
5.3.b_ab_a_g_s$24$(not in LMFDB)
5.3.b_b_ag_ad_aj$24$(not in LMFDB)
5.3.b_b_ag_m_s$24$(not in LMFDB)
5.3.b_e_ad_aj_abk$24$(not in LMFDB)
5.3.b_e_ad_p_a$24$(not in LMFDB)
5.3.b_h_a_s_as$24$(not in LMFDB)
5.3.c_ac_a_ad_abk$24$(not in LMFDB)
5.3.c_b_g_j_a$24$(not in LMFDB)
5.3.c_e_m_v_bk$24$(not in LMFDB)
5.3.c_h_s_bh_cu$24$(not in LMFDB)
5.3.c_k_y_bt_ee$24$(not in LMFDB)
5.3.d_af_ay_g_dm$24$(not in LMFDB)
5.3.d_ac_ap_j_cu$24$(not in LMFDB)
5.3.d_ab_am_ag_s$24$(not in LMFDB)
5.3.d_b_ag_m_cc$24$(not in LMFDB)
5.3.d_c_ad_j_bk$24$(not in LMFDB)
5.3.d_e_d_p_bk$24$(not in LMFDB)
5.3.d_f_g_y_cc$24$(not in LMFDB)
5.3.d_h_m_s_s$24$(not in LMFDB)
5.3.d_i_p_bn_cu$24$(not in LMFDB)
5.3.d_l_y_cc_dm$24$(not in LMFDB)
5.3.e_h_a_abe_acu$24$(not in LMFDB)
5.3.e_h_a_abb_acu$24$(not in LMFDB)
5.3.e_l_y_bq_cu$24$(not in LMFDB)
5.3.e_n_y_bw_cu$24$(not in LMFDB)
5.3.e_t_bw_ew_ii$24$(not in LMFDB)
5.3.f_e_ap_av_a$24$(not in LMFDB)
5.3.f_h_a_j_bt$24$(not in LMFDB)
5.3.f_k_p_bn_dm$24$(not in LMFDB)
5.3.f_k_p_bt_ee$24$(not in LMFDB)
5.3.f_n_be_cr_ff$24$(not in LMFDB)
5.3.f_q_bt_dv_gy$24$(not in LMFDB)
5.3.h_t_m_aco_ahq$24$(not in LMFDB)
5.3.h_t_m_acl_ahh$24$(not in LMFDB)
5.3.h_w_bh_j_abk$24$(not in LMFDB)
5.3.h_x_bw_da_ew$24$(not in LMFDB)
5.3.h_z_cc_dg_ew$24$(not in LMFDB)
5.3.h_bc_cx_gd_lc$24$(not in LMFDB)
5.3.h_bf_ds_ja_ri$24$(not in LMFDB)
5.3.i_bf_dg_hh_nw$24$(not in LMFDB)
5.3.j_bi_cl_bt_a$24$(not in LMFDB)
5.3.j_bm_dv_hh_mm$24$(not in LMFDB)
5.3.l_cd_gm_of_zz$24$(not in LMFDB)
5.3.n_de_mp_biz_csq$24$(not in LMFDB)
5.3.ae_k_av_bt_adm$72$(not in LMFDB)
5.3.ae_k_ad_abb_dm$72$(not in LMFDB)
5.3.ac_b_ap_bb_aj$72$(not in LMFDB)
5.3.ac_b_d_aj_j$72$(not in LMFDB)
5.3.a_ac_aj_j_s$72$(not in LMFDB)
5.3.a_ac_j_j_as$72$(not in LMFDB)
5.3.a_c_aj_j_as$72$(not in LMFDB)
5.3.a_c_j_j_s$72$(not in LMFDB)
5.3.c_b_ad_aj_aj$72$(not in LMFDB)
5.3.c_b_p_bb_j$72$(not in LMFDB)
5.3.e_k_d_abb_adm$72$(not in LMFDB)
5.3.e_k_v_bt_dm$72$(not in LMFDB)