Properties

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

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Invariants

Base field:  $\F_{3}$
Dimension:  $5$
L-polynomial:  $( 1 - 2 x + 3 x^{2} )( 1 - 3 x + 3 x^{2} )^{2}( 1 - 2 x + 2 x^{2} - 6 x^{3} + 9 x^{4} )$
Frobenius angles:  $\pm0.116139763599$, $\pm0.166666666667$, $\pm0.166666666667$, $\pm0.304086723985$, $\pm0.616139763599$
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
$A(\F_{q^r})$ 8 47040 12989312 5087846400 1227099817768 223632308551680 52379898422025112 13009098341862604800 3019576655024956750976 717837007930413343896000

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -6 6 24 110 334 792 2290 7006 20112 59046

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_c 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 2 $\times$ 1.531441.azi $\times$ 1.531441.sk 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.ag_q_abg_cx_aga$2$(not in LMFDB)
5.3.ag_q_aq_av_dg$2$(not in LMFDB)
5.3.ae_g_ae_j_ay$2$(not in LMFDB)
5.3.ac_a_e_d_am$2$(not in LMFDB)
5.3.a_ac_ai_j_y$2$(not in LMFDB)
5.3.a_ac_i_j_ay$2$(not in LMFDB)
5.3.c_a_ae_d_m$2$(not in LMFDB)
5.3.e_g_e_j_y$2$(not in LMFDB)
5.3.g_q_q_av_adg$2$(not in LMFDB)
5.3.g_q_bg_cx_ga$2$(not in LMFDB)
5.3.k_bw_fs_nb_ym$2$(not in LMFDB)
5.3.ah_bb_acy_gs_ams$3$(not in LMFDB)
5.3.ae_p_abo_dm_agm$3$(not in LMFDB)
5.3.ab_d_ae_g_ag$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
5.3.ag_q_abg_cx_aga$2$(not in LMFDB)
5.3.ag_q_aq_av_dg$2$(not in LMFDB)
5.3.ae_g_ae_j_ay$2$(not in LMFDB)
5.3.ac_a_e_d_am$2$(not in LMFDB)
5.3.a_ac_ai_j_y$2$(not in LMFDB)
5.3.a_ac_i_j_ay$2$(not in LMFDB)
5.3.c_a_ae_d_m$2$(not in LMFDB)
5.3.e_g_e_j_y$2$(not in LMFDB)
5.3.g_q_q_av_adg$2$(not in LMFDB)
5.3.g_q_bg_cx_ga$2$(not in LMFDB)
5.3.k_bw_fs_nb_ym$2$(not in LMFDB)
5.3.ah_bb_acy_gs_ams$3$(not in LMFDB)
5.3.ae_p_abo_dm_agm$3$(not in LMFDB)
5.3.ab_d_ae_g_ag$3$(not in LMFDB)
5.3.ae_m_abc_cl_aeq$4$(not in LMFDB)
5.3.a_e_ai_p_ay$4$(not in LMFDB)
5.3.a_e_i_p_y$4$(not in LMFDB)
5.3.e_m_bc_cl_eq$4$(not in LMFDB)
5.3.ad_h_au_bq_aco$6$(not in LMFDB)
5.3.ad_h_ae_ag_be$6$(not in LMFDB)
5.3.a_h_ai_s_abw$6$(not in LMFDB)
5.3.a_h_i_s_bw$6$(not in LMFDB)
5.3.b_d_e_g_g$6$(not in LMFDB)
5.3.d_h_e_ag_abe$6$(not in LMFDB)
5.3.d_h_u_bq_co$6$(not in LMFDB)
5.3.e_p_bo_dm_gm$6$(not in LMFDB)
5.3.h_bb_cy_gs_ms$6$(not in LMFDB)
5.3.ai_ba_abi_av_eq$8$(not in LMFDB)
5.3.ai_bi_adu_il_aps$8$(not in LMFDB)
5.3.ae_c_k_d_abw$8$(not in LMFDB)
5.3.ae_k_aw_bz_ads$8$(not in LMFDB)
5.3.ac_ae_o_j_aci$8$(not in LMFDB)
5.3.ac_c_c_d_am$8$(not in LMFDB)
5.3.ac_e_ac_j_am$8$(not in LMFDB)
5.3.ac_k_ao_bz_aci$8$(not in LMFDB)
5.3.c_ae_ao_j_ci$8$(not in LMFDB)
5.3.c_c_ac_d_m$8$(not in LMFDB)
5.3.c_e_c_j_m$8$(not in LMFDB)
5.3.c_k_o_bz_ci$8$(not in LMFDB)
5.3.e_c_ak_d_bw$8$(not in LMFDB)
5.3.e_k_w_bz_ds$8$(not in LMFDB)
5.3.i_ba_bi_av_aeq$8$(not in LMFDB)
5.3.i_bi_du_il_ps$8$(not in LMFDB)
5.3.ae_d_i_as_y$12$(not in LMFDB)
5.3.a_af_ai_g_bw$12$(not in LMFDB)
5.3.a_af_i_g_abw$12$(not in LMFDB)
5.3.e_d_ai_as_ay$12$(not in LMFDB)
5.3.af_l_ak_ag_be$24$(not in LMFDB)
5.3.af_t_aby_ek_aic$24$(not in LMFDB)
5.3.ae_j_aq_bk_acu$24$(not in LMFDB)
5.3.ac_ah_u_m_adg$24$(not in LMFDB)
5.3.ac_ab_i_g_abk$24$(not in LMFDB)
5.3.ac_b_e_am_m$24$(not in LMFDB)
5.3.ac_f_ae_a_m$24$(not in LMFDB)
5.3.ac_h_ai_be_abk$24$(not in LMFDB)
5.3.ac_n_au_cu_adg$24$(not in LMFDB)
5.3.ab_ab_ac_g_g$24$(not in LMFDB)
5.3.ab_h_ak_be_abq$24$(not in LMFDB)
5.3.a_b_ai_m_a$24$(not in LMFDB)
5.3.a_b_i_m_a$24$(not in LMFDB)
5.3.b_ab_c_g_ag$24$(not in LMFDB)
5.3.b_h_k_be_bq$24$(not in LMFDB)
5.3.c_ah_au_m_dg$24$(not in LMFDB)
5.3.c_ab_ai_g_bk$24$(not in LMFDB)
5.3.c_b_ae_am_am$24$(not in LMFDB)
5.3.c_f_e_a_am$24$(not in LMFDB)
5.3.c_h_i_be_bk$24$(not in LMFDB)
5.3.c_n_u_cu_dg$24$(not in LMFDB)
5.3.e_j_q_bk_cu$24$(not in LMFDB)
5.3.f_l_k_ag_abe$24$(not in LMFDB)
5.3.f_t_by_ek_ic$24$(not in LMFDB)