Properties

Label 4.5.ao_dp_aoo_bnk
Base Field $\F_{5}$
Dimension $4$
Ordinary Yes
$p$-rank $4$
Principally polarizable Yes
Contains a Jacobian No

Learn more about

Invariants

Base field:  $\F_{5}$
Dimension:  $4$
L-polynomial:  $( 1 - 4 x + 5 x^{2} )^{2}( 1 - 3 x + 5 x^{2} )^{2}$
Frobenius angles:  $\pm0.147583617650$, $\pm0.147583617650$, $\pm0.265942140215$, $\pm0.265942140215$
Angle rank:  $2$ (numerical)

This isogeny class is not simple.

Newton polygon

This isogeny class is ordinary.

$p$-rank:  $4$
Slopes:  $[0, 0, 0, 0, 1, 1, 1, 1]$

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
$A(\F_{q^r})$ 36 291600 308634624 186624000000 103876170945156 60838550898278400 37298113629404912964 23271370696986624000000 14559654807532466321826816 9101424859935705708138090000

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -8 16 154 752 3392 15946 78224 390432 1954162 9772576

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{5}$
The isogeny class factors as 1.5.ae 2 $\times$ 1.5.ad 2 and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is:
All geometric endomorphisms are defined over $\F_{5}$.

Base change

This is a primitive isogeny class.

Twists

Below are some of the twists of this isogeny class.
TwistExtension DegreeCommon base change
4.5.ai_bb_abw_cy$2$(not in LMFDB)
4.5.ag_n_g_acm$2$(not in LMFDB)
4.5.ac_ad_ag_cm$2$(not in LMFDB)
4.5.a_af_a_bs$2$(not in LMFDB)
4.5.c_ad_g_cm$2$(not in LMFDB)
4.5.g_n_ag_acm$2$(not in LMFDB)
4.5.i_bb_bw_cy$2$(not in LMFDB)
4.5.o_dp_oo_bnk$2$(not in LMFDB)
4.5.af_g_v_adi$3$(not in LMFDB)
4.5.ac_g_a_t$3$(not in LMFDB)
4.5.h_bb_dg_ig$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
4.5.ai_bb_abw_cy$2$(not in LMFDB)
4.5.ag_n_g_acm$2$(not in LMFDB)
4.5.ac_ad_ag_cm$2$(not in LMFDB)
4.5.a_af_a_bs$2$(not in LMFDB)
4.5.c_ad_g_cm$2$(not in LMFDB)
4.5.g_n_ag_acm$2$(not in LMFDB)
4.5.i_bb_bw_cy$2$(not in LMFDB)
4.5.o_dp_oo_bnk$2$(not in LMFDB)
4.5.af_g_v_adi$3$(not in LMFDB)
4.5.ac_g_a_t$3$(not in LMFDB)
4.5.h_bb_dg_ig$3$(not in LMFDB)
4.5.am_cv_akw_bcy$4$(not in LMFDB)
4.5.ak_cf_aic_vk$4$(not in LMFDB)
4.5.ai_z_abg_y$4$(not in LMFDB)
4.5.ai_bh_adm_ia$4$(not in LMFDB)
4.5.ag_r_ay_bg$4$(not in LMFDB)
4.5.ag_t_abk_cq$4$(not in LMFDB)
4.5.ag_z_aco_gi$4$(not in LMFDB)
4.5.ae_j_g_abg$4$(not in LMFDB)
4.5.ae_n_aq_bk$4$(not in LMFDB)
4.5.ae_p_ay_cm$4$(not in LMFDB)
4.5.ac_b_ai_bw$4$(not in LMFDB)
4.5.ac_d_am_ca$4$(not in LMFDB)
4.5.ac_j_as_cy$4$(not in LMFDB)
4.5.a_ah_a_ce$4$(not in LMFDB)
4.5.a_b_ag_bg$4$(not in LMFDB)
4.5.a_b_g_bg$4$(not in LMFDB)
4.5.a_f_a_bs$4$(not in LMFDB)
4.5.a_h_a_ce$4$(not in LMFDB)
4.5.c_b_i_bw$4$(not in LMFDB)
4.5.c_d_m_ca$4$(not in LMFDB)
4.5.c_j_s_cy$4$(not in LMFDB)
4.5.e_j_ag_abg$4$(not in LMFDB)
4.5.e_n_q_bk$4$(not in LMFDB)
4.5.e_p_y_cm$4$(not in LMFDB)
4.5.g_r_y_bg$4$(not in LMFDB)
4.5.g_t_bk_cq$4$(not in LMFDB)
4.5.g_z_co_gi$4$(not in LMFDB)
4.5.i_z_bg_y$4$(not in LMFDB)
4.5.i_bh_dm_ia$4$(not in LMFDB)
4.5.k_cf_ic_vk$4$(not in LMFDB)
4.5.m_cv_kw_bcy$4$(not in LMFDB)
4.5.al_cc_agj_pe$6$(not in LMFDB)
4.5.ak_cc_ahk_tf$6$(not in LMFDB)
4.5.ah_bb_adg_ig$6$(not in LMFDB)
4.5.ae_m_ay_cj$6$(not in LMFDB)
4.5.ad_ac_d_ba$6$(not in LMFDB)
4.5.ab_d_m_aba$6$(not in LMFDB)
4.5.b_d_am_aba$6$(not in LMFDB)
4.5.c_g_a_t$6$(not in LMFDB)
4.5.d_ac_ad_ba$6$(not in LMFDB)
4.5.e_m_y_cj$6$(not in LMFDB)
4.5.f_g_av_adi$6$(not in LMFDB)
4.5.k_cc_hk_tf$6$(not in LMFDB)
4.5.l_cc_gj_pe$6$(not in LMFDB)
4.5.ag_l_s_ady$8$(not in LMFDB)
4.5.ag_bb_ada_hu$8$(not in LMFDB)
4.5.a_aj_a_cg$8$(not in LMFDB)
4.5.a_ah_a_bq$8$(not in LMFDB)
4.5.a_h_a_bq$8$(not in LMFDB)
4.5.a_j_a_cg$8$(not in LMFDB)
4.5.g_l_as_ady$8$(not in LMFDB)
4.5.g_bb_da_hu$8$(not in LMFDB)
4.5.aj_bo_aet_lq$12$(not in LMFDB)
4.5.ai_be_acu_fv$12$(not in LMFDB)
4.5.ah_be_adp_is$12$(not in LMFDB)
4.5.af_j_abe_ec$12$(not in LMFDB)
4.5.af_m_abn_eo$12$(not in LMFDB)
4.5.ae_g_y_adl$12$(not in LMFDB)
4.5.ae_k_aq_bn$12$(not in LMFDB)
4.5.ad_e_p_acg$12$(not in LMFDB)
4.5.ad_k_abh_cw$12$(not in LMFDB)
4.5.ac_ac_ai_bz$12$(not in LMFDB)
4.5.ac_a_am_bx$12$(not in LMFDB)
4.5.ab_ad_g_ao$12$(not in LMFDB)
4.5.ab_a_ad_ac$12$(not in LMFDB)
4.5.ab_g_v_ao$12$(not in LMFDB)
4.5.b_ad_ag_ao$12$(not in LMFDB)
4.5.b_a_d_ac$12$(not in LMFDB)
4.5.b_g_av_ao$12$(not in LMFDB)
4.5.c_ac_i_bz$12$(not in LMFDB)
4.5.c_a_m_bx$12$(not in LMFDB)
4.5.d_e_ap_acg$12$(not in LMFDB)
4.5.d_k_bh_cw$12$(not in LMFDB)
4.5.e_g_ay_adl$12$(not in LMFDB)
4.5.e_k_q_bn$12$(not in LMFDB)
4.5.f_j_be_ec$12$(not in LMFDB)
4.5.f_m_bn_eo$12$(not in LMFDB)
4.5.h_be_dp_is$12$(not in LMFDB)
4.5.i_be_cu_fv$12$(not in LMFDB)
4.5.j_bo_et_lq$12$(not in LMFDB)
4.5.ad_ae_j_s$24$(not in LMFDB)
4.5.ad_m_abn_de$24$(not in LMFDB)
4.5.d_ae_aj_s$24$(not in LMFDB)
4.5.d_m_bn_de$24$(not in LMFDB)