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

Learn more about

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.

Point counts of the abelian variety

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

Point counts of the (virtual) curve

$r$ 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:
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.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.
TwistExtension DegreeCommon 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)