Properties

Label 5.3.al_ck_aiv_xl_abuq
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:  $( 1 - x + 3 x^{2} )( 1 - 3 x + 3 x^{2} )^{2}( 1 - 2 x + 3 x^{2} )^{2}$
Frobenius angles:  $\pm0.166666666667$, $\pm0.166666666667$, $\pm0.304086723985$, $\pm0.304086723985$, $\pm0.406785250661$
Angle rank:  $2$ (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
$A(\F_{q^r})$ 12 105840 40755456 5723827200 916112728212 207050758225920 51659660696201724 12552784305636556800 2991573062959305017088 717912132567305475769200

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -7 13 56 121 263 736 2261 6769 19928 59053

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{3}$
The isogeny class factors as 1.3.ad 2 $\times$ 1.3.ac 2 $\times$ 1.3.ab 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 2 $\times$ 1.729.ak $\times$ 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.aj_bq_afb_lx_awq$2$(not in LMFDB)
5.3.ah_ba_acn_ez_aiu$2$(not in LMFDB)
5.3.af_o_abf_cr_afc$2$(not in LMFDB)
5.3.af_o_at_j_m$2$(not in LMFDB)
5.3.ad_g_an_bh_aci$2$(not in LMFDB)
5.3.ad_g_af_j_am$2$(not in LMFDB)
5.3.ab_c_al_v_am$2$(not in LMFDB)
5.3.ab_c_b_j_am$2$(not in LMFDB)
5.3.b_c_ab_j_m$2$(not in LMFDB)
5.3.b_c_l_v_m$2$(not in LMFDB)
5.3.d_g_f_j_m$2$(not in LMFDB)
5.3.d_g_n_bh_ci$2$(not in LMFDB)
5.3.f_o_t_j_am$2$(not in LMFDB)
5.3.f_o_bf_cr_fc$2$(not in LMFDB)
5.3.h_ba_cn_ez_iu$2$(not in LMFDB)
5.3.j_bq_fb_lx_wq$2$(not in LMFDB)
5.3.l_ck_iv_xl_buq$2$(not in LMFDB)
5.3.ai_bm_aeu_lx_axc$3$(not in LMFDB)
5.3.af_l_ae_abn_eh$3$(not in LMFDB)
5.3.af_o_at_j_m$3$(not in LMFDB)
5.3.af_x_acm_gg_ali$3$(not in LMFDB)
5.3.ac_f_c_ap_bw$3$(not in LMFDB)
5.3.ac_i_ae_p_m$3$(not in LMFDB)
5.3.b_ab_i_j_ap$3$(not in LMFDB)
5.3.b_c_l_v_m$3$(not in LMFDB)
5.3.b_i_r_bb_dg$3$(not in LMFDB)
5.3.e_l_bg_cr_eq$3$(not in LMFDB)
5.3.h_x_ce_ez_jv$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
5.3.aj_bq_afb_lx_awq$2$(not in LMFDB)
5.3.ah_ba_acn_ez_aiu$2$(not in LMFDB)
5.3.af_o_abf_cr_afc$2$(not in LMFDB)
5.3.af_o_at_j_m$2$(not in LMFDB)
5.3.ad_g_an_bh_aci$2$(not in LMFDB)
5.3.ad_g_af_j_am$2$(not in LMFDB)
5.3.ab_c_al_v_am$2$(not in LMFDB)
5.3.ab_c_b_j_am$2$(not in LMFDB)
5.3.b_c_ab_j_m$2$(not in LMFDB)
5.3.b_c_l_v_m$2$(not in LMFDB)
5.3.d_g_f_j_m$2$(not in LMFDB)
5.3.d_g_n_bh_ci$2$(not in LMFDB)
5.3.f_o_t_j_am$2$(not in LMFDB)
5.3.f_o_bf_cr_fc$2$(not in LMFDB)
5.3.h_ba_cn_ez_iu$2$(not in LMFDB)
5.3.j_bq_fb_lx_wq$2$(not in LMFDB)
5.3.l_ck_iv_xl_buq$2$(not in LMFDB)
5.3.ai_bm_aeu_lx_axc$3$(not in LMFDB)
5.3.af_l_ae_abn_eh$3$(not in LMFDB)
5.3.af_o_at_j_m$3$(not in LMFDB)
5.3.af_x_acm_gg_ali$3$(not in LMFDB)
5.3.ac_f_c_ap_bw$3$(not in LMFDB)
5.3.ac_i_ae_p_m$3$(not in LMFDB)
5.3.b_ab_i_j_ap$3$(not in LMFDB)
5.3.b_c_l_v_m$3$(not in LMFDB)
5.3.b_i_r_bb_dg$3$(not in LMFDB)
5.3.e_l_bg_cr_eq$3$(not in LMFDB)
5.3.h_x_ce_ez_jv$3$(not in LMFDB)
5.3.ah_w_abl_bh_ay$4$(not in LMFDB)
5.3.af_k_al_v_abw$4$(not in LMFDB)
5.3.af_u_abx_eh_ahk$4$(not in LMFDB)
5.3.ad_m_ax_cl_ads$4$(not in LMFDB)
5.3.ab_ac_f_j_ay$4$(not in LMFDB)
5.3.ab_e_ab_p_am$4$(not in LMFDB)
5.3.ab_i_af_bn_ay$4$(not in LMFDB)
5.3.b_ac_af_j_y$4$(not in LMFDB)
5.3.b_e_b_p_m$4$(not in LMFDB)
5.3.b_i_f_bn_y$4$(not in LMFDB)
5.3.d_m_x_cl_ds$4$(not in LMFDB)
5.3.f_k_l_v_bw$4$(not in LMFDB)
5.3.f_u_bx_eh_hk$4$(not in LMFDB)
5.3.h_w_bl_bh_y$4$(not in LMFDB)
5.3.aj_bn_aei_jp_arx$6$(not in LMFDB)
5.3.ah_x_ace_ez_ajv$6$(not in LMFDB)
5.3.ag_v_acg_ez_ajg$6$(not in LMFDB)
5.3.ag_y_acq_gd_alo$6$(not in LMFDB)
5.3.ae_l_abg_cr_aeq$6$(not in LMFDB)
5.3.ae_o_abg_cr_aeq$6$(not in LMFDB)
5.3.ad_d_ae_j_ap$6$(not in LMFDB)
5.3.ad_d_e_ap_bh$6$(not in LMFDB)
5.3.ad_m_abf_cl_afc$6$(not in LMFDB)
5.3.ad_p_abg_dm_afi$6$(not in LMFDB)
5.3.ac_i_aq_bn_aci$6$(not in LMFDB)
5.3.ab_ab_ai_j_p$6$(not in LMFDB)
5.3.ab_i_ar_bb_adg$6$(not in LMFDB)
5.3.ab_l_ai_cc_abe$6$(not in LMFDB)
5.3.a_d_ae_ad_ay$6$(not in LMFDB)
5.3.a_d_e_ad_y$6$(not in LMFDB)
5.3.a_g_ae_v_ay$6$(not in LMFDB)
5.3.a_g_e_v_y$6$(not in LMFDB)
5.3.b_l_i_cc_be$6$(not in LMFDB)
5.3.c_f_ac_ap_abw$6$(not in LMFDB)
5.3.c_i_e_p_am$6$(not in LMFDB)
5.3.c_i_q_bn_ci$6$(not in LMFDB)
5.3.d_d_ae_ap_abh$6$(not in LMFDB)
5.3.d_d_e_j_p$6$(not in LMFDB)
5.3.d_m_bf_cl_fc$6$(not in LMFDB)
5.3.d_p_bg_dm_fi$6$(not in LMFDB)
5.3.e_o_bg_cr_eq$6$(not in LMFDB)
5.3.f_l_e_abn_aeh$6$(not in LMFDB)
5.3.f_x_cm_gg_li$6$(not in LMFDB)
5.3.g_v_cg_ez_jg$6$(not in LMFDB)
5.3.g_y_cq_gd_lo$6$(not in LMFDB)
5.3.i_bm_eu_lx_xc$6$(not in LMFDB)
5.3.j_bn_ei_jp_rx$6$(not in LMFDB)
5.3.al_ci_aih_vp_abqs$8$(not in LMFDB)
5.3.aj_bo_aer_kz_ava$8$(not in LMFDB)
5.3.af_m_ar_j_g$8$(not in LMFDB)
5.3.af_s_abv_dv_ahe$8$(not in LMFDB)
5.3.ad_e_ah_j_ag$8$(not in LMFDB)
5.3.ad_e_b_ap_bq$8$(not in LMFDB)
5.3.ad_k_az_bz_ady$8$(not in LMFDB)
5.3.ab_a_ab_ad_be$8$(not in LMFDB)
5.3.b_a_b_ad_abe$8$(not in LMFDB)
5.3.d_e_ab_ap_abq$8$(not in LMFDB)
5.3.d_e_h_j_g$8$(not in LMFDB)
5.3.d_k_z_bz_dy$8$(not in LMFDB)
5.3.f_m_r_j_ag$8$(not in LMFDB)
5.3.f_s_bv_dv_he$8$(not in LMFDB)
5.3.j_bo_er_kz_va$8$(not in LMFDB)
5.3.l_ci_ih_vp_bqs$8$(not in LMFDB)
5.3.af_l_ae_abq_ek$12$(not in LMFDB)
5.3.ae_k_aq_v_ay$12$(not in LMFDB)
5.3.ad_a_f_aj_y$12$(not in LMFDB)
5.3.ad_d_e_as_be$12$(not in LMFDB)
5.3.ad_j_aw_bt_adp$12$(not in LMFDB)
5.3.ac_e_ai_p_am$12$(not in LMFDB)
5.3.ab_af_i_g_abe$12$(not in LMFDB)
5.3.ab_ae_af_d_bw$12$(not in LMFDB)
5.3.ab_ab_e_ag_ag$12$(not in LMFDB)
5.3.ab_f_ao_v_abz$12$(not in LMFDB)
5.3.ab_h_ae_s_ag$12$(not in LMFDB)
5.3.b_af_ai_g_be$12$(not in LMFDB)
5.3.b_ae_f_d_abw$12$(not in LMFDB)
5.3.b_ab_ae_ag_g$12$(not in LMFDB)
5.3.b_f_o_v_bz$12$(not in LMFDB)
5.3.b_h_e_s_g$12$(not in LMFDB)
5.3.c_e_i_p_m$12$(not in LMFDB)
5.3.d_a_af_aj_ay$12$(not in LMFDB)
5.3.d_d_ae_as_abe$12$(not in LMFDB)
5.3.d_j_w_bt_dp$12$(not in LMFDB)
5.3.e_k_q_v_y$12$(not in LMFDB)
5.3.f_l_e_abq_aek$12$(not in LMFDB)
5.3.ai_bk_aem_kz_avg$24$(not in LMFDB)
5.3.ag_w_acm_fr_akq$24$(not in LMFDB)
5.3.af_j_ac_abk_dy$24$(not in LMFDB)
5.3.af_p_abg_cc_adm$24$(not in LMFDB)
5.3.af_r_abi_ci_adm$24$(not in LMFDB)
5.3.af_v_ack_fo_akw$24$(not in LMFDB)
5.3.ad_b_c_am_bq$24$(not in LMFDB)
5.3.ad_g_an_bb_acc$24$(not in LMFDB)
5.3.ad_h_aq_be_acc$24$(not in LMFDB)
5.3.ad_j_ao_bk_acc$24$(not in LMFDB)
5.3.ad_n_abi_cu_afu$24$(not in LMFDB)
5.3.ac_g_ai_d_am$24$(not in LMFDB)
5.3.ab_b_c_m_as$24$(not in LMFDB)
5.3.ab_c_al_p_as$24$(not in LMFDB)
5.3.ab_f_ac_y_as$24$(not in LMFDB)
5.3.a_e_ae_ad_ay$24$(not in LMFDB)
5.3.a_e_e_ad_y$24$(not in LMFDB)
5.3.b_b_ac_m_s$24$(not in LMFDB)
5.3.b_c_l_p_s$24$(not in LMFDB)
5.3.b_f_c_y_s$24$(not in LMFDB)
5.3.c_g_i_d_m$24$(not in LMFDB)
5.3.d_b_ac_am_abq$24$(not in LMFDB)
5.3.d_g_n_bb_cc$24$(not in LMFDB)
5.3.d_h_q_be_cc$24$(not in LMFDB)
5.3.d_j_o_bk_cc$24$(not in LMFDB)
5.3.d_n_bi_cu_fu$24$(not in LMFDB)
5.3.f_j_c_abk_ady$24$(not in LMFDB)
5.3.f_p_bg_cc_dm$24$(not in LMFDB)
5.3.f_r_bi_ci_dm$24$(not in LMFDB)
5.3.f_v_ck_fo_kw$24$(not in LMFDB)
5.3.g_w_cm_fr_kq$24$(not in LMFDB)
5.3.i_bk_em_kz_vg$24$(not in LMFDB)