Properties

Label 4.5.ao_dn_any_blk
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:  $( 1 - 4 x + 5 x^{2} )^{2}( 1 - 6 x + 17 x^{2} - 30 x^{3} + 25 x^{4} )$
Frobenius angles:  $\pm0.0512862249088$, $\pm0.147583617650$, $\pm0.147583617650$, $\pm0.384619558242$
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
$A(\F_{q^r})$ 28 221200 230463856 148816281600 94313975316988 60307689652537600 37824215428924710268 23460952075775882035200 14573350564538393946716272 9090913800345378830015530000

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -8 12 118 608 3092 15810 79316 393600 1955998 9761292

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{5}$
The isogeny class factors as 1.5.ae 2 $\times$ 2.5.ag_r 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 $\overline{\F}_{5}$
The base change of $A$ to $\F_{5^{6}}$ is 1.15625.afm 2 $\times$ 1.15625.ja 2 . The endomorphism algebra for each factor is:
All geometric endomorphisms are defined over $\F_{5^{6}}$.
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
4.5.ag_l_g_aca$2$(not in LMFDB)
4.5.ac_af_k_m$2$(not in LMFDB)
4.5.c_af_ak_m$2$(not in LMFDB)
4.5.g_l_ag_aca$2$(not in LMFDB)
4.5.o_dn_ny_blk$2$(not in LMFDB)
4.5.ai_bc_ace_dy$3$(not in LMFDB)
4.5.ac_af_k_m$3$(not in LMFDB)
4.5.ac_e_ai_ad$3$(not in LMFDB)
4.5.e_n_bc_cu$3$(not in LMFDB)
4.5.k_ca_hc_sj$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
4.5.ag_l_g_aca$2$(not in LMFDB)
4.5.ac_af_k_m$2$(not in LMFDB)
4.5.c_af_ak_m$2$(not in LMFDB)
4.5.g_l_ag_aca$2$(not in LMFDB)
4.5.o_dn_ny_blk$2$(not in LMFDB)
4.5.ai_bc_ace_dy$3$(not in LMFDB)
4.5.ac_af_k_m$3$(not in LMFDB)
4.5.ac_e_ai_ad$3$(not in LMFDB)
4.5.e_n_bc_cu$3$(not in LMFDB)
4.5.k_ca_hc_sj$3$(not in LMFDB)
4.5.am_ct_akk_bbo$4$(not in LMFDB)
4.5.ak_cd_ahu_ui$4$(not in LMFDB)
4.5.ai_bf_adi_hw$4$(not in LMFDB)
4.5.ag_x_aco_fw$4$(not in LMFDB)
4.5.ae_h_c_abk$4$(not in LMFDB)
4.5.ac_h_aba_bw$4$(not in LMFDB)
4.5.a_ab_ag_ae$4$(not in LMFDB)
4.5.a_ab_g_ae$4$(not in LMFDB)
4.5.c_h_ba_bw$4$(not in LMFDB)
4.5.e_h_ac_abk$4$(not in LMFDB)
4.5.g_x_co_fw$4$(not in LMFDB)
4.5.i_bf_di_hw$4$(not in LMFDB)
4.5.k_cd_hu_ui$4$(not in LMFDB)
4.5.m_ct_kk_bbo$4$(not in LMFDB)
4.5.ak_ca_ahc_sj$6$(not in LMFDB)
4.5.ae_n_abc_cu$6$(not in LMFDB)
4.5.a_ae_a_bm$6$(not in LMFDB)
4.5.c_e_i_ad$6$(not in LMFDB)
4.5.i_bc_ce_dy$6$(not in LMFDB)
4.5.ag_j_s_adi$8$(not in LMFDB)
4.5.ag_z_ada_he$8$(not in LMFDB)
4.5.g_j_as_adi$8$(not in LMFDB)
4.5.g_z_da_he$8$(not in LMFDB)
4.5.ai_y_ay_ac$12$(not in LMFDB)
4.5.ai_bc_acq_fx$12$(not in LMFDB)
4.5.ag_q_as_o$12$(not in LMFDB)
4.5.ag_u_abq_di$12$(not in LMFDB)
4.5.ae_e_u_adj$12$(not in LMFDB)
4.5.ae_j_am_bc$12$(not in LMFDB)
4.5.ae_m_am_w$12$(not in LMFDB)
4.5.ae_q_abc_da$12$(not in LMFDB)
4.5.ac_ad_ag_ca$12$(not in LMFDB)
4.5.ac_a_ag_bu$12$(not in LMFDB)
4.5.ac_b_ao_bw$12$(not in LMFDB)
4.5.ac_e_ao_cc$12$(not in LMFDB)
4.5.a_ai_a_ck$12$(not in LMFDB)
4.5.a_e_a_bm$12$(not in LMFDB)
4.5.a_i_a_ck$12$(not in LMFDB)
4.5.c_ad_g_ca$12$(not in LMFDB)
4.5.c_a_g_bu$12$(not in LMFDB)
4.5.c_b_o_bw$12$(not in LMFDB)
4.5.c_e_o_cc$12$(not in LMFDB)
4.5.e_e_au_adj$12$(not in LMFDB)
4.5.e_j_m_bc$12$(not in LMFDB)
4.5.e_m_m_w$12$(not in LMFDB)
4.5.e_q_bc_da$12$(not in LMFDB)
4.5.g_q_s_o$12$(not in LMFDB)
4.5.g_u_bq_di$12$(not in LMFDB)
4.5.i_y_y_ac$12$(not in LMFDB)
4.5.i_bc_cq_fx$12$(not in LMFDB)
4.5.am_co_aiu_wg$24$(not in LMFDB)
4.5.ak_by_ago_qs$24$(not in LMFDB)
4.5.ai_bj_aem_lm$24$(not in LMFDB)
4.5.ai_bm_aey_mk$24$(not in LMFDB)
4.5.ag_p_abq_es$24$(not in LMFDB)
4.5.ag_s_acc_fq$24$(not in LMFDB)
4.5.ae_a_m_ao$24$(not in LMFDB)
4.5.ae_c_e_c$24$(not in LMFDB)
4.5.ae_c_u_ack$24$(not in LMFDB)
4.5.ae_o_abs_du$24$(not in LMFDB)
4.5.ae_q_aca_ek$24$(not in LMFDB)
4.5.ac_ab_k_abm$24$(not in LMFDB)
4.5.ac_c_ac_ao$24$(not in LMFDB)
4.5.ac_c_o_abu$24$(not in LMFDB)
4.5.a_ak_a_co$24$(not in LMFDB)
4.5.a_ag_a_bi$24$(not in LMFDB)
4.5.a_d_am_aw$24$(not in LMFDB)
4.5.a_d_m_aw$24$(not in LMFDB)
4.5.a_g_ay_c$24$(not in LMFDB)
4.5.a_g_a_bi$24$(not in LMFDB)
4.5.a_g_y_c$24$(not in LMFDB)
4.5.a_k_a_co$24$(not in LMFDB)
4.5.c_ab_ak_abm$24$(not in LMFDB)
4.5.c_c_ao_abu$24$(not in LMFDB)
4.5.c_c_c_ao$24$(not in LMFDB)
4.5.e_a_am_ao$24$(not in LMFDB)
4.5.e_c_au_ack$24$(not in LMFDB)
4.5.e_c_ae_c$24$(not in LMFDB)
4.5.e_o_bs_du$24$(not in LMFDB)
4.5.e_q_ca_ek$24$(not in LMFDB)
4.5.g_p_bq_es$24$(not in LMFDB)
4.5.g_s_cc_fq$24$(not in LMFDB)
4.5.i_bj_em_lm$24$(not in LMFDB)
4.5.i_bm_ey_mk$24$(not in LMFDB)
4.5.k_by_go_qs$24$(not in LMFDB)
4.5.m_co_iu_wg$24$(not in LMFDB)