Properties

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

Invariants

 Base field: $\F_{5}$ Dimension: $4$ L-polynomial: $( 1 + x + 5 x^{2} )( 1 - 4 x + 5 x^{2} )^{3}$ Frobenius angles: $\pm0.147583617650$, $\pm0.147583617650$, $\pm0.147583617650$, $\pm0.571783146564$ 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.

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 56 280000 203374976 155975680000 105940726822616 62554075118080000 37783585372224468056 23489648805575393280000 14602778182723702213671296 9092594955955713993175000000

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ -5 17 100 637 3455 16382 79235 394077 1959940 9763097

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{5}$
 The isogeny class factors as 1.5.ae 3 $\times$ 1.5.b and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is: 1.5.ae 3 : $\mathrm{M}_{3}($$$\Q(\sqrt{-1})$$$)$ 1.5.b : $$\Q(\sqrt{-19})$$.
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.
 Twist Extension Degree Common base change 4.5.an_dc_alv_bfi $2$ (not in LMFDB) 4.5.af_i_f_abi $2$ (not in LMFDB) 4.5.ad_a_d_o $2$ (not in LMFDB) 4.5.d_a_ad_o $2$ (not in LMFDB) 4.5.f_i_af_abi $2$ (not in LMFDB) 4.5.l_ce_gz_re $2$ (not in LMFDB) 4.5.n_dc_lv_bfi $2$ (not in LMFDB) 4.5.b_f_ae_ae $3$ (not in LMFDB)
Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 4.5.an_dc_alv_bfi $2$ (not in LMFDB) 4.5.af_i_f_abi $2$ (not in LMFDB) 4.5.ad_a_d_o $2$ (not in LMFDB) 4.5.d_a_ad_o $2$ (not in LMFDB) 4.5.f_i_af_abi $2$ (not in LMFDB) 4.5.l_ce_gz_re $2$ (not in LMFDB) 4.5.n_dc_lv_bfi $2$ (not in LMFDB) 4.5.b_f_ae_ae $3$ (not in LMFDB) 4.5.al_ck_aiv_xe $4$ (not in LMFDB) 4.5.aj_bq_aff_na $4$ (not in LMFDB) 4.5.aj_bw_agp_re $4$ (not in LMFDB) 4.5.ah_ba_acv_gw $4$ (not in LMFDB) 4.5.ah_bg_adx_ju $4$ (not in LMFDB) 4.5.ah_bm_aev_na $4$ (not in LMFDB) 4.5.af_o_abr_es $4$ (not in LMFDB) 4.5.af_u_acd_fe $4$ (not in LMFDB) 4.5.af_ba_act_hu $4$ (not in LMFDB) 4.5.ad_g_d_aw $4$ (not in LMFDB) 4.5.ad_m_abh_di $4$ (not in LMFDB) 4.5.ad_s_abh_es $4$ (not in LMFDB) 4.5.ab_c_b_c $4$ (not in LMFDB) 4.5.ab_i_at_bu $4$ (not in LMFDB) 4.5.ab_i_n_o $4$ (not in LMFDB) 4.5.ab_o_al_du $4$ (not in LMFDB) 4.5.b_c_ab_c $4$ (not in LMFDB) 4.5.b_i_an_o $4$ (not in LMFDB) 4.5.b_i_t_bu $4$ (not in LMFDB) 4.5.b_o_l_du $4$ (not in LMFDB) 4.5.d_g_ad_aw $4$ (not in LMFDB) 4.5.d_m_bh_di $4$ (not in LMFDB) 4.5.d_s_bh_es $4$ (not in LMFDB) 4.5.f_o_br_es $4$ (not in LMFDB) 4.5.f_u_cd_fe $4$ (not in LMFDB) 4.5.f_ba_ct_hu $4$ (not in LMFDB) 4.5.h_ba_cv_gw $4$ (not in LMFDB) 4.5.h_bg_dx_ju $4$ (not in LMFDB) 4.5.h_bm_ev_na $4$ (not in LMFDB) 4.5.j_bq_ff_na $4$ (not in LMFDB) 4.5.j_bw_gp_re $4$ (not in LMFDB) 4.5.l_ck_iv_xe $4$ (not in LMFDB) 4.5.aj_bt_aga_po $6$ (not in LMFDB) 4.5.ah_bd_ado_jc $6$ (not in LMFDB) 4.5.ab_f_ae_e $6$ (not in LMFDB) 4.5.ab_f_e_ae $6$ (not in LMFDB) 4.5.b_f_e_e $6$ (not in LMFDB) 4.5.h_bd_do_jc $6$ (not in LMFDB) 4.5.j_bt_ga_po $6$ (not in LMFDB) 4.5.af_g_p_ack $8$ (not in LMFDB) 4.5.af_w_acn_gg $8$ (not in LMFDB) 4.5.ad_ac_j_c $8$ (not in LMFDB) 4.5.ad_e_j_abu $8$ (not in LMFDB) 4.5.ad_o_abn_du $8$ (not in LMFDB) 4.5.ad_u_abn_fq $8$ (not in LMFDB) 4.5.ab_a_d_ao $8$ (not in LMFDB) 4.5.ab_q_an_ek $8$ (not in LMFDB) 4.5.b_a_ad_ao $8$ (not in LMFDB) 4.5.b_q_n_ek $8$ (not in LMFDB) 4.5.d_ac_aj_c $8$ (not in LMFDB) 4.5.d_e_aj_abu $8$ (not in LMFDB) 4.5.d_o_bn_du $8$ (not in LMFDB) 4.5.d_u_bn_fq $8$ (not in LMFDB) 4.5.f_g_ap_ack $8$ (not in LMFDB) 4.5.f_w_cn_gg $8$ (not in LMFDB) 4.5.ah_x_acg_fg $12$ (not in LMFDB) 4.5.ah_bj_aem_lq $12$ (not in LMFDB) 4.5.af_l_abi_ea $12$ (not in LMFDB) 4.5.af_r_abu_du $12$ (not in LMFDB) 4.5.af_x_acq_gw $12$ (not in LMFDB) 4.5.ad_d_s_acm $12$ (not in LMFDB) 4.5.ad_j_abe_ck $12$ (not in LMFDB) 4.5.ad_p_abk_du $12$ (not in LMFDB) 4.5.ab_ab_k_aq $12$ (not in LMFDB) 4.5.ab_f_aw_w $12$ (not in LMFDB) 4.5.ab_f_w_aw $12$ (not in LMFDB) 4.5.ab_l_au_ck $12$ (not in LMFDB) 4.5.b_ab_ak_aq $12$ (not in LMFDB) 4.5.b_f_aw_aw $12$ (not in LMFDB) 4.5.b_f_w_w $12$ (not in LMFDB) 4.5.b_l_u_ck $12$ (not in LMFDB) 4.5.d_d_as_acm $12$ (not in LMFDB) 4.5.d_j_be_ck $12$ (not in LMFDB) 4.5.d_p_bk_du $12$ (not in LMFDB) 4.5.f_l_bi_ea $12$ (not in LMFDB) 4.5.f_r_bu_du $12$ (not in LMFDB) 4.5.f_x_cq_gw $12$ (not in LMFDB) 4.5.h_x_cg_fg $12$ (not in LMFDB) 4.5.h_bj_em_lq $12$ (not in LMFDB)