Properties

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

Learn more about

Invariants

Base field:  $\F_{3}$
Dimension:  $5$
L-polynomial:  $( 1 - 2 x + 3 x^{2} )( 1 - 3 x + 3 x^{2} )^{2}( 1 - 2 x + x^{2} - 6 x^{3} + 9 x^{4} )$
Frobenius angles:  $\pm0.0292466093486$, $\pm0.166666666667$, $\pm0.166666666667$, $\pm0.304086723985$, $\pm0.637420057318$
Angle rank:  $1$ (numerical)

This isogeny class is not simple.

Newton polygon

$p$-rank:  $3$
Slopes:  $[0, 0, 0, 1/2, 1/2, 1/2, 1/2, 1, 1, 1]$

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
$A(\F_{q^r})$ 6 33516 9652608 4395422304 1036558465206 196698220314624 49780651221603042 12463487624210313600 2926266810943148717184 712025827391529486333036

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -6 4 18 100 294 700 2178 6724 19494 58564

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{3}$
The isogeny class factors as 1.3.ad 2 $\times$ 1.3.ac $\times$ 2.3.ac_b 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 3 $\times$ 1.729.cc 2 . 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.ag_p_abc_cr_afu$2$(not in LMFDB)
5.3.ag_p_ai_abz_fu$2$(not in LMFDB)
5.3.ae_f_ac_j_abe$2$(not in LMFDB)
5.3.ac_ab_i_ad_ag$2$(not in LMFDB)
5.3.a_ad_ak_j_be$2$(not in LMFDB)
5.3.a_ad_k_j_abe$2$(not in LMFDB)
5.3.c_ab_ai_ad_g$2$(not in LMFDB)
5.3.e_f_c_j_be$2$(not in LMFDB)
5.3.g_p_i_abz_afu$2$(not in LMFDB)
5.3.g_p_bc_cr_fu$2$(not in LMFDB)
5.3.k_bv_fk_lx_vy$2$(not in LMFDB)
5.3.ah_ba_act_gd_alo$3$(not in LMFDB)
5.3.ae_f_ac_j_abe$3$(not in LMFDB)
5.3.ae_i_ao_bn_adg$3$(not in LMFDB)
5.3.ae_o_abm_dd_aga$3$(not in LMFDB)
5.3.ab_c_af_d_am$3$(not in LMFDB)
5.3.ab_f_ai_y_abe$3$(not in LMFDB)
5.3.c_ab_ai_ad_g$3$(not in LMFDB)
5.3.c_c_ac_j_y$3$(not in LMFDB)
5.3.c_l_q_cc_ci$3$(not in LMFDB)
5.3.f_r_bo_dg_fu$3$(not in LMFDB)
5.3.i_bg_de_gd_kq$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
5.3.ag_p_abc_cr_afu$2$(not in LMFDB)
5.3.ag_p_ai_abz_fu$2$(not in LMFDB)
5.3.ae_f_ac_j_abe$2$(not in LMFDB)
5.3.ac_ab_i_ad_ag$2$(not in LMFDB)
5.3.a_ad_ak_j_be$2$(not in LMFDB)
5.3.a_ad_k_j_abe$2$(not in LMFDB)
5.3.c_ab_ai_ad_g$2$(not in LMFDB)
5.3.e_f_c_j_be$2$(not in LMFDB)
5.3.g_p_i_abz_afu$2$(not in LMFDB)
5.3.g_p_bc_cr_fu$2$(not in LMFDB)
5.3.k_bv_fk_lx_vy$2$(not in LMFDB)
5.3.ah_ba_act_gd_alo$3$(not in LMFDB)
5.3.ae_f_ac_j_abe$3$(not in LMFDB)
5.3.ae_i_ao_bn_adg$3$(not in LMFDB)
5.3.ae_o_abm_dd_aga$3$(not in LMFDB)
5.3.ab_c_af_d_am$3$(not in LMFDB)
5.3.ab_f_ai_y_abe$3$(not in LMFDB)
5.3.c_ab_ai_ad_g$3$(not in LMFDB)
5.3.c_c_ac_j_y$3$(not in LMFDB)
5.3.c_l_q_cc_ci$3$(not in LMFDB)
5.3.f_r_bo_dg_fu$3$(not in LMFDB)
5.3.i_bg_de_gd_kq$3$(not in LMFDB)
5.3.ae_l_aba_cf_aek$4$(not in LMFDB)
5.3.a_d_ak_j_abe$4$(not in LMFDB)
5.3.a_d_k_j_be$4$(not in LMFDB)
5.3.e_l_ba_cf_ek$4$(not in LMFDB)
5.3.am_cu_aks_bdf_acgq$6$(not in LMFDB)
5.3.aj_bt_afw_ou_abcw$6$(not in LMFDB)
5.3.ai_bg_ade_gd_akq$6$(not in LMFDB)
5.3.ag_s_aba_j_y$6$(not in LMFDB)
5.3.ag_bb_adc_hq_aoi$6$(not in LMFDB)
5.3.af_r_abo_dg_afu$6$(not in LMFDB)
5.3.ad_g_at_bn_aci$6$(not in LMFDB)
5.3.ad_g_b_av_ci$6$(not in LMFDB)
5.3.ad_j_ai_m_g$6$(not in LMFDB)
5.3.ac_c_c_j_ay$6$(not in LMFDB)
5.3.ac_l_aq_cc_aci$6$(not in LMFDB)
5.3.a_a_ak_p_m$6$(not in LMFDB)
5.3.a_a_k_p_am$6$(not in LMFDB)
5.3.a_g_ak_j_aci$6$(not in LMFDB)
5.3.a_g_k_j_ci$6$(not in LMFDB)
5.3.b_c_f_d_m$6$(not in LMFDB)
5.3.b_f_i_y_be$6$(not in LMFDB)
5.3.d_g_ab_av_aci$6$(not in LMFDB)
5.3.d_g_t_bn_ci$6$(not in LMFDB)
5.3.d_j_i_m_ag$6$(not in LMFDB)
5.3.e_i_o_bn_dg$6$(not in LMFDB)
5.3.e_o_bm_dd_ga$6$(not in LMFDB)
5.3.g_s_ba_j_ay$6$(not in LMFDB)
5.3.g_bb_dc_hq_oi$6$(not in LMFDB)
5.3.h_ba_ct_gd_lo$6$(not in LMFDB)
5.3.j_bt_fw_ou_bcw$6$(not in LMFDB)
5.3.m_cu_ks_bdf_cgq$6$(not in LMFDB)
5.3.ai_bc_aby_bn_am$12$(not in LMFDB)
5.3.ag_p_ai_acc_ga$12$(not in LMFDB)
5.3.ag_y_ack_ff_ajg$12$(not in LMFDB)
5.3.af_n_au_y_abe$12$(not in LMFDB)
5.3.ae_c_k_ap_m$12$(not in LMFDB)
5.3.ae_e_c_p_aci$12$(not in LMFDB)
5.3.ac_af_q_g_aci$12$(not in LMFDB)
5.3.ac_ac_k_j_abw$12$(not in LMFDB)
5.3.ac_ab_i_ag_am$12$(not in LMFDB)
5.3.ac_e_ac_p_ay$12$(not in LMFDB)
5.3.ac_h_ai_s_am$12$(not in LMFDB)
5.3.ac_i_ak_bn_abw$12$(not in LMFDB)
5.3.ab_b_ae_m_ag$12$(not in LMFDB)
5.3.a_ag_ak_j_ci$12$(not in LMFDB)
5.3.a_ag_k_j_aci$12$(not in LMFDB)
5.3.b_b_e_m_g$12$(not in LMFDB)
5.3.c_af_aq_g_ci$12$(not in LMFDB)
5.3.c_ac_ak_j_bw$12$(not in LMFDB)
5.3.c_ab_ai_ag_m$12$(not in LMFDB)
5.3.c_e_c_p_y$12$(not in LMFDB)
5.3.c_h_i_s_m$12$(not in LMFDB)
5.3.c_i_k_bn_bw$12$(not in LMFDB)
5.3.e_c_ak_ap_am$12$(not in LMFDB)
5.3.e_e_ac_p_ci$12$(not in LMFDB)
5.3.f_n_u_y_be$12$(not in LMFDB)
5.3.g_p_i_acc_aga$12$(not in LMFDB)
5.3.g_y_ck_ff_jg$12$(not in LMFDB)
5.3.i_bc_by_bn_m$12$(not in LMFDB)
5.3.am_cs_akc_bax_acbo$24$(not in LMFDB)
5.3.aj_br_afm_nq_abao$24$(not in LMFDB)
5.3.ai_be_acw_fr_ake$24$(not in LMFDB)
5.3.ag_n_ae_abw_fc$24$(not in LMFDB)
5.3.ag_q_aw_j_m$24$(not in LMFDB)
5.3.ag_t_abo_co_aee$24$(not in LMFDB)
5.3.ag_v_abs_cu_aee$24$(not in LMFDB)
5.3.ag_w_acg_et_aiu$24$(not in LMFDB)
5.3.ag_z_acy_gy_ank$24$(not in LMFDB)
5.3.af_p_abm_da_afi$24$(not in LMFDB)
5.3.ae_g_c_av_bw$24$(not in LMFDB)
5.3.ae_i_ao_bh_acu$24$(not in LMFDB)
5.3.ad_h_ak_g_ag$24$(not in LMFDB)
5.3.ac_ad_e_a_m$24$(not in LMFDB)
5.3.ac_a_ac_j_am$24$(not in LMFDB)
5.3.ac_b_e_m_abk$24$(not in LMFDB)
5.3.ac_d_ai_s_abk$24$(not in LMFDB)
5.3.ac_f_ae_y_abk$24$(not in LMFDB)
5.3.ac_g_ao_bb_aci$24$(not in LMFDB)
5.3.ac_j_au_bk_adg$24$(not in LMFDB)
5.3.ab_d_c_ag_be$24$(not in LMFDB)
5.3.a_ac_ac_d_y$24$(not in LMFDB)
5.3.a_ac_c_d_ay$24$(not in LMFDB)
5.3.a_a_ak_j_a$24$(not in LMFDB)
5.3.a_a_k_j_a$24$(not in LMFDB)
5.3.b_d_ac_ag_abe$24$(not in LMFDB)
5.3.c_ad_ae_a_am$24$(not in LMFDB)
5.3.c_a_c_j_m$24$(not in LMFDB)
5.3.c_b_ae_m_bk$24$(not in LMFDB)
5.3.c_d_i_s_bk$24$(not in LMFDB)
5.3.c_f_e_y_bk$24$(not in LMFDB)
5.3.c_g_o_bb_ci$24$(not in LMFDB)
5.3.c_j_u_bk_dg$24$(not in LMFDB)
5.3.d_h_k_g_g$24$(not in LMFDB)
5.3.e_g_ac_av_abw$24$(not in LMFDB)
5.3.e_i_o_bh_cu$24$(not in LMFDB)
5.3.f_p_bm_da_fi$24$(not in LMFDB)
5.3.g_n_e_abw_afc$24$(not in LMFDB)
5.3.g_q_w_j_am$24$(not in LMFDB)
5.3.g_t_bo_co_ee$24$(not in LMFDB)
5.3.g_v_bs_cu_ee$24$(not in LMFDB)
5.3.g_w_cg_et_iu$24$(not in LMFDB)
5.3.g_z_cy_gy_nk$24$(not in LMFDB)
5.3.i_be_cw_fr_ke$24$(not in LMFDB)
5.3.j_br_fm_nq_bao$24$(not in LMFDB)
5.3.m_cs_kc_bax_cbo$24$(not in LMFDB)