Properties

Label 4.5.am_cr_ajs_zg
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:  $( 1 - 4 x + 5 x^{2} )^{2}( 1 - 4 x + 11 x^{2} - 20 x^{3} + 25 x^{4} )$
Frobenius angles:  $\pm0.147583617650$, $\pm0.147583617650$, $\pm0.185749715683$, $\pm0.480916950984$
Angle rank:  $1$ (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
$A(\F_{q^r})$ 52 317200 251539600 156234956800 102588049661812 63272170368160000 38056342149202802932 23345947240459252531200 14551929298156324491648400 9095389395817645702197130000

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -6 20 126 640 3354 16562 79794 391680 1953126 9766100

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{5}$
The isogeny class factors as 1.5.ae 2 $\times$ 2.5.ae_l 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.ja 4 and its endomorphism algebra is $\mathrm{M}_{4}($\(\Q(\sqrt{-1}) \)$)$
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.ae_f_ae_q$2$(not in LMFDB)
4.5.ae_f_e_aq$2$(not in LMFDB)
4.5.e_f_ae_aq$2$(not in LMFDB)
4.5.e_f_e_q$2$(not in LMFDB)
4.5.m_cr_js_zg$2$(not in LMFDB)
4.5.a_am_a_di$3$(not in LMFDB)
4.5.a_g_a_l$3$(not in LMFDB)
4.5.m_cr_js_zg$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
4.5.ae_f_ae_q$2$(not in LMFDB)
4.5.ae_f_e_aq$2$(not in LMFDB)
4.5.e_f_ae_aq$2$(not in LMFDB)
4.5.e_f_e_q$2$(not in LMFDB)
4.5.m_cr_js_zg$2$(not in LMFDB)
4.5.a_am_a_di$3$(not in LMFDB)
4.5.a_g_a_l$3$(not in LMFDB)
4.5.m_cr_js_zg$3$(not in LMFDB)
4.5.ak_bp_adq_hc$4$(not in LMFDB)
4.5.ak_cb_ahg_su$4$(not in LMFDB)
4.5.ai_bd_acs_fw$4$(not in LMFDB)
4.5.ai_bp_afk_oa$4$(not in LMFDB)
4.5.ag_j_be_afg$4$(not in LMFDB)
4.5.ag_v_aci_fw$4$(not in LMFDB)
4.5.ag_v_acc_em$4$(not in LMFDB)
4.5.ae_f_aw_dk$4$(not in LMFDB)
4.5.ae_f_w_adk$4$(not in LMFDB)
4.5.ae_r_abs_em$4$(not in LMFDB)
4.5.ac_ah_c_ce$4$(not in LMFDB)
4.5.ac_f_aw_bs$4$(not in LMFDB)
4.5.ac_f_ae_i$4$(not in LMFDB)
4.5.ac_f_e_ai$4$(not in LMFDB)
4.5.ac_f_w_abs$4$(not in LMFDB)
4.5.a_ad_ag_i$4$(not in LMFDB)
4.5.a_ad_g_i$4$(not in LMFDB)
4.5.a_j_am_bs$4$(not in LMFDB)
4.5.a_j_m_bs$4$(not in LMFDB)
4.5.c_ah_ac_ce$4$(not in LMFDB)
4.5.c_f_aw_abs$4$(not in LMFDB)
4.5.c_f_ae_ai$4$(not in LMFDB)
4.5.c_f_e_i$4$(not in LMFDB)
4.5.c_f_w_bs$4$(not in LMFDB)
4.5.e_f_aw_adk$4$(not in LMFDB)
4.5.e_f_w_dk$4$(not in LMFDB)
4.5.e_r_bs_em$4$(not in LMFDB)
4.5.g_j_abe_afg$4$(not in LMFDB)
4.5.g_v_cc_em$4$(not in LMFDB)
4.5.g_v_ci_fw$4$(not in LMFDB)
4.5.i_bd_cs_fw$4$(not in LMFDB)
4.5.i_bp_fk_oa$4$(not in LMFDB)
4.5.k_bp_dq_hc$4$(not in LMFDB)
4.5.k_cb_hg_su$4$(not in LMFDB)
4.5.aq_em_atc_cao$6$(not in LMFDB)
4.5.ai_u_i_aec$6$(not in LMFDB)
4.5.ai_bm_aey_mt$6$(not in LMFDB)
4.5.i_u_ai_aec$6$(not in LMFDB)
4.5.i_bm_ey_mt$6$(not in LMFDB)
4.5.q_em_tc_cao$6$(not in LMFDB)
4.5.ae_d_m_abm$8$(not in LMFDB)
4.5.ae_t_aca_fi$8$(not in LMFDB)
4.5.ac_aj_g_cg$8$(not in LMFDB)
4.5.ac_h_aba_bq$8$(not in LMFDB)
4.5.c_aj_ag_cg$8$(not in LMFDB)
4.5.c_h_ba_bq$8$(not in LMFDB)
4.5.e_d_am_abm$8$(not in LMFDB)
4.5.e_t_ca_fi$8$(not in LMFDB)
4.5.ao_do_aog_bmk$12$(not in LMFDB)
4.5.am_cu_akq_bcg$12$(not in LMFDB)
4.5.ak_bs_aeo_kc$12$(not in LMFDB)
4.5.ak_ce_ahy_uw$12$(not in LMFDB)
4.5.ai_bg_adk_hy$12$(not in LMFDB)
4.5.ai_bs_afw_pq$12$(not in LMFDB)
4.5.ag_m_g_acg$12$(not in LMFDB)
4.5.ag_s_abw_ep$12$(not in LMFDB)
4.5.ag_y_aco_gc$12$(not in LMFDB)
4.5.ae_c_aq_dn$12$(not in LMFDB)
4.5.ae_i_abc_dq$12$(not in LMFDB)
4.5.ae_i_e_abi$12$(not in LMFDB)
4.5.ae_u_abs_fe$12$(not in LMFDB)
4.5.ac_ae_c_bm$12$(not in LMFDB)
4.5.ac_c_q_abp$12$(not in LMFDB)
4.5.ac_i_aw_ck$12$(not in LMFDB)
4.5.ac_i_k_ac$12$(not in LMFDB)
4.5.a_ag_a_l$12$(not in LMFDB)
4.5.a_a_a_o$12$(not in LMFDB)
4.5.a_m_a_di$12$(not in LMFDB)
4.5.c_ae_ac_bm$12$(not in LMFDB)
4.5.c_c_aq_abp$12$(not in LMFDB)
4.5.c_i_ak_ac$12$(not in LMFDB)
4.5.c_i_w_ck$12$(not in LMFDB)
4.5.e_c_q_dn$12$(not in LMFDB)
4.5.e_i_ae_abi$12$(not in LMFDB)
4.5.e_i_bc_dq$12$(not in LMFDB)
4.5.e_u_bs_fe$12$(not in LMFDB)
4.5.g_m_ag_acg$12$(not in LMFDB)
4.5.g_s_bw_ep$12$(not in LMFDB)
4.5.g_y_co_gc$12$(not in LMFDB)
4.5.i_bg_dk_hy$12$(not in LMFDB)
4.5.i_bs_fw_pq$12$(not in LMFDB)
4.5.k_bs_eo_kc$12$(not in LMFDB)
4.5.k_ce_hy_uw$12$(not in LMFDB)
4.5.m_cu_kq_bcg$12$(not in LMFDB)
4.5.o_do_og_bmk$12$(not in LMFDB)
4.5.ai_s_y_agc$24$(not in LMFDB)
4.5.ai_bi_aea_jy$24$(not in LMFDB)
4.5.ag_k_s_adq$24$(not in LMFDB)
4.5.ag_ba_ada_hm$24$(not in LMFDB)
4.5.ae_g_m_ack$24$(not in LMFDB)
4.5.ae_w_aca_gg$24$(not in LMFDB)
4.5.ac_ag_g_bi$24$(not in LMFDB)
4.5.ac_k_aba_co$24$(not in LMFDB)
4.5.a_aq_a_ek$24$(not in LMFDB)
4.5.a_ao_a_du$24$(not in LMFDB)
4.5.a_ai_a_bn$24$(not in LMFDB)
4.5.a_ac_a_c$24$(not in LMFDB)
4.5.a_a_a_ao$24$(not in LMFDB)
4.5.a_c_a_c$24$(not in LMFDB)
4.5.a_i_a_bn$24$(not in LMFDB)
4.5.a_o_a_du$24$(not in LMFDB)
4.5.a_q_a_ek$24$(not in LMFDB)
4.5.c_ag_ag_bi$24$(not in LMFDB)
4.5.c_k_ba_co$24$(not in LMFDB)
4.5.e_g_am_ack$24$(not in LMFDB)
4.5.e_w_ca_gg$24$(not in LMFDB)
4.5.g_k_as_adq$24$(not in LMFDB)
4.5.g_ba_da_hm$24$(not in LMFDB)
4.5.i_s_ay_agc$24$(not in LMFDB)
4.5.i_bi_ea_jy$24$(not in LMFDB)
4.5.ae_l_ay_bp$30$(not in LMFDB)
4.5.e_l_y_bp$30$(not in LMFDB)
4.5.a_a_a_abw$48$(not in LMFDB)
4.5.a_a_a_bw$48$(not in LMFDB)
4.5.ac_ab_m_at$60$(not in LMFDB)
4.5.c_ab_am_at$60$(not in LMFDB)