Properties

Label 5.3.am_ct_akk_bcb_acec
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:  $( 1 - 2 x + 3 x^{2} )( 1 - x + 3 x^{2} )( 1 - 3 x + 3 x^{2} )^{3}$
Frobenius angles:  $\pm0.166666666667$, $\pm0.166666666667$, $\pm0.166666666667$, $\pm0.304086723985$, $\pm0.406785250661$
Angle rank:  $2$ (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
$A(\F_{q^r})$ 6 61740 30030336 5425711200 1025894832006 237321336913920 55763924890428978 12773919445824700800 2962972938074416823808 709169165824859455646700

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -8 8 46 116 292 836 2428 6884 19738 58328

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{3}$
The isogeny class factors as 1.3.ad 3 $\times$ 1.3.ac $\times$ 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 $\times$ 1.729.ak $\times$ 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.ak_bx_aga_of_abba$2$(not in LMFDB)
5.3.ai_bf_ada_fx_akk$2$(not in LMFDB)
5.3.ag_r_abk_dd_agg$2$(not in LMFDB)
5.3.ag_r_ay_j_s$2$(not in LMFDB)
5.3.ae_h_ag_j_as$2$(not in LMFDB)
5.3.ac_b_a_j_as$2$(not in LMFDB)
5.3.a_ab_ag_j_s$2$(not in LMFDB)
5.3.a_ab_g_j_as$2$(not in LMFDB)
5.3.c_b_a_j_s$2$(not in LMFDB)
5.3.e_h_g_j_s$2$(not in LMFDB)
5.3.g_r_y_j_as$2$(not in LMFDB)
5.3.g_r_bk_dd_gg$2$(not in LMFDB)
5.3.i_bf_da_fx_kk$2$(not in LMFDB)
5.3.k_bx_ga_of_bba$2$(not in LMFDB)
5.3.m_ct_kk_bcb_cec$2$(not in LMFDB)
5.3.aj_bs_afr_of_abbs$3$(not in LMFDB)
5.3.ag_r_ay_j_s$3$(not in LMFDB)
5.3.ag_ba_ada_hh_anw$3$(not in LMFDB)
5.3.ad_i_aj_j_a$3$(not in LMFDB)
5.3.ad_r_abk_ee_agg$3$(not in LMFDB)
5.3.a_ab_g_j_as$3$(not in LMFDB)
5.3.a_i_g_bb_bk$3$(not in LMFDB)
5.3.d_i_v_bt_cu$3$(not in LMFDB)
5.3.g_r_bk_dd_gg$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
5.3.ak_bx_aga_of_abba$2$(not in LMFDB)
5.3.ai_bf_ada_fx_akk$2$(not in LMFDB)
5.3.ag_r_abk_dd_agg$2$(not in LMFDB)
5.3.ag_r_ay_j_s$2$(not in LMFDB)
5.3.ae_h_ag_j_as$2$(not in LMFDB)
5.3.ac_b_a_j_as$2$(not in LMFDB)
5.3.a_ab_ag_j_s$2$(not in LMFDB)
5.3.a_ab_g_j_as$2$(not in LMFDB)
5.3.c_b_a_j_s$2$(not in LMFDB)
5.3.e_h_g_j_s$2$(not in LMFDB)
5.3.g_r_y_j_as$2$(not in LMFDB)
5.3.g_r_bk_dd_gg$2$(not in LMFDB)
5.3.i_bf_da_fx_kk$2$(not in LMFDB)
5.3.k_bx_ga_of_bba$2$(not in LMFDB)
5.3.m_ct_kk_bcb_cec$2$(not in LMFDB)
5.3.aj_bs_afr_of_abbs$3$(not in LMFDB)
5.3.ag_r_ay_j_s$3$(not in LMFDB)
5.3.ag_ba_ada_hh_anw$3$(not in LMFDB)
5.3.ad_i_aj_j_a$3$(not in LMFDB)
5.3.ad_r_abk_ee_agg$3$(not in LMFDB)
5.3.a_ab_g_j_as$3$(not in LMFDB)
5.3.a_i_g_bb_bk$3$(not in LMFDB)
5.3.d_i_v_bt_cu$3$(not in LMFDB)
5.3.g_r_bk_dd_gg$3$(not in LMFDB)
5.3.ag_x_aci_ez_aja$4$(not in LMFDB)
5.3.ae_n_abe_cr_aew$4$(not in LMFDB)
5.3.ac_h_am_bh_acc$4$(not in LMFDB)
5.3.a_f_ag_v_as$4$(not in LMFDB)
5.3.a_f_g_v_s$4$(not in LMFDB)
5.3.c_h_m_bh_cc$4$(not in LMFDB)
5.3.e_n_be_cr_ew$4$(not in LMFDB)
5.3.g_x_ci_ez_ja$4$(not in LMFDB)
5.3.ah_bc_add_hh_anw$6$(not in LMFDB)
5.3.af_q_abn_dd_afo$6$(not in LMFDB)
5.3.ae_q_abq_dv_agy$6$(not in LMFDB)
5.3.ad_i_av_bt_acu$6$(not in LMFDB)
5.3.ac_k_as_bt_acu$6$(not in LMFDB)
5.3.ab_e_ad_j_a$6$(not in LMFDB)
5.3.ab_n_am_cu_acc$6$(not in LMFDB)
5.3.a_i_ag_bb_abk$6$(not in LMFDB)
5.3.b_e_d_j_a$6$(not in LMFDB)
5.3.b_n_m_cu_cc$6$(not in LMFDB)
5.3.c_k_s_bt_cu$6$(not in LMFDB)
5.3.d_i_j_j_a$6$(not in LMFDB)
5.3.d_r_bk_ee_gg$6$(not in LMFDB)
5.3.e_q_bq_dv_gy$6$(not in LMFDB)
5.3.f_q_bn_dd_fo$6$(not in LMFDB)
5.3.g_ba_da_hh_nw$6$(not in LMFDB)
5.3.h_bc_dd_hh_nw$6$(not in LMFDB)
5.3.j_bs_fr_of_bbs$6$(not in LMFDB)
5.3.ad_i_as_bk_acu$9$(not in LMFDB)
5.3.ad_i_a_as_cu$9$(not in LMFDB)
5.3.ag_o_ag_abz_fo$12$(not in LMFDB)
5.3.ae_e_g_av_bk$12$(not in LMFDB)
5.3.ad_f_a_ay_cc$12$(not in LMFDB)
5.3.ad_o_abb_cx_aee$12$(not in LMFDB)
5.3.ac_ac_g_ad_a$12$(not in LMFDB)
5.3.ab_b_a_am_s$12$(not in LMFDB)
5.3.ab_k_aj_bz_abk$12$(not in LMFDB)
5.3.a_ae_ag_d_bk$12$(not in LMFDB)
5.3.a_ae_g_d_abk$12$(not in LMFDB)
5.3.b_b_a_am_as$12$(not in LMFDB)
5.3.b_k_j_bz_bk$12$(not in LMFDB)
5.3.c_ac_ag_ad_a$12$(not in LMFDB)
5.3.d_f_a_ay_acc$12$(not in LMFDB)
5.3.d_o_bb_cx_ee$12$(not in LMFDB)
5.3.e_e_ag_av_abk$12$(not in LMFDB)
5.3.g_o_g_abz_afo$12$(not in LMFDB)
5.3.ab_e_am_s_abk$18$(not in LMFDB)
5.3.ab_e_g_a_bk$18$(not in LMFDB)
5.3.b_e_ag_a_abk$18$(not in LMFDB)
5.3.b_e_m_s_bk$18$(not in LMFDB)
5.3.d_i_a_as_acu$18$(not in LMFDB)
5.3.d_i_s_bk_cu$18$(not in LMFDB)
5.3.ag_u_abq_cr_aee$24$(not in LMFDB)
5.3.ae_k_as_bn_acu$24$(not in LMFDB)
5.3.ad_l_as_bq_acc$24$(not in LMFDB)
5.3.ac_e_ag_v_abk$24$(not in LMFDB)
5.3.ab_h_ag_be_as$24$(not in LMFDB)
5.3.a_c_ag_p_a$24$(not in LMFDB)
5.3.a_c_g_p_a$24$(not in LMFDB)
5.3.b_h_g_be_s$24$(not in LMFDB)
5.3.c_e_g_v_bk$24$(not in LMFDB)
5.3.d_l_s_bq_cc$24$(not in LMFDB)
5.3.e_k_s_bn_cu$24$(not in LMFDB)
5.3.g_u_bq_cr_ee$24$(not in LMFDB)