Properties

Label 4.5.an_de_aml_bhi
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:  $( 1 - 3 x + 5 x^{2} )( 1 - 2 x + 5 x^{2} )( 1 - 4 x + 5 x^{2} )^{2}$
Frobenius angles:  $\pm0.147583617650$, $\pm0.147583617650$, $\pm0.265942140215$, $\pm0.352416382350$
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
$A(\F_{q^r})$ 48 345600 317207808 176947200000 99339951101808 60212639880806400 37513870763864295408 23403120802607923200000 14584385684232990885973248 9098187204184464865659840000

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -7 21 158 717 3253 15786 78673 392637 1957478 9769101

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{5}$
The isogeny class factors as 1.5.ae 2 $\times$ 1.5.ad $\times$ 1.5.ac 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 $\F_{5^{4}}$ is 1.625.o 3 $\times$ 1.625.bx. The endomorphism algebra for each factor is:
All geometric endomorphisms are defined over $\F_{5^{4}}$.
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.aj_bm_adz_ja$2$(not in LMFDB)
4.5.ah_w_abp_cw$2$(not in LMFDB)
4.5.af_k_f_abu$2$(not in LMFDB)
4.5.ad_c_an_co$2$(not in LMFDB)
4.5.ab_ac_b_ba$2$(not in LMFDB)
4.5.b_ac_ab_ba$2$(not in LMFDB)
4.5.d_c_n_co$2$(not in LMFDB)
4.5.f_k_af_abu$2$(not in LMFDB)
4.5.h_w_bp_cw$2$(not in LMFDB)
4.5.j_bm_dz_ja$2$(not in LMFDB)
4.5.n_de_ml_bhi$2$(not in LMFDB)
4.5.ab_h_e_ba$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
4.5.aj_bm_adz_ja$2$(not in LMFDB)
4.5.ah_w_abp_cw$2$(not in LMFDB)
4.5.af_k_f_abu$2$(not in LMFDB)
4.5.ad_c_an_co$2$(not in LMFDB)
4.5.ab_ac_b_ba$2$(not in LMFDB)
4.5.b_ac_ab_ba$2$(not in LMFDB)
4.5.d_c_n_co$2$(not in LMFDB)
4.5.f_k_af_abu$2$(not in LMFDB)
4.5.h_w_bp_cw$2$(not in LMFDB)
4.5.j_bm_dz_ja$2$(not in LMFDB)
4.5.n_de_ml_bhi$2$(not in LMFDB)
4.5.ab_h_e_ba$3$(not in LMFDB)
4.5.ap_ea_aqr_btm$4$(not in LMFDB)
4.5.al_cm_ajh_yo$4$(not in LMFDB)
4.5.aj_bg_acd_da$4$(not in LMFDB)
4.5.aj_by_agx_sg$4$(not in LMFDB)
4.5.ah_q_h_ade$4$(not in LMFDB)
4.5.ah_bc_acz_ha$4$(not in LMFDB)
4.5.af_q_abf_ck$4$(not in LMFDB)
4.5.af_w_acd_fq$4$(not in LMFDB)
4.5.ad_i_az_da$4$(not in LMFDB)
4.5.ad_i_h_as$4$(not in LMFDB)
4.5.ad_o_ar_co$4$(not in LMFDB)
4.5.ab_ai_b_ck$4$(not in LMFDB)
4.5.ab_e_al_bm$4$(not in LMFDB)
4.5.ab_k_al_cw$4$(not in LMFDB)
4.5.b_ai_ab_ck$4$(not in LMFDB)
4.5.b_e_l_bm$4$(not in LMFDB)
4.5.b_k_l_cw$4$(not in LMFDB)
4.5.d_i_ah_as$4$(not in LMFDB)
4.5.d_i_z_da$4$(not in LMFDB)
4.5.d_o_r_co$4$(not in LMFDB)
4.5.f_q_bf_ck$4$(not in LMFDB)
4.5.f_w_cd_fq$4$(not in LMFDB)
4.5.h_q_ah_ade$4$(not in LMFDB)
4.5.h_bc_cz_ha$4$(not in LMFDB)
4.5.j_bg_cd_da$4$(not in LMFDB)
4.5.j_by_gx_sg$4$(not in LMFDB)
4.5.l_cm_jh_yo$4$(not in LMFDB)
4.5.p_ea_qr_btm$4$(not in LMFDB)
4.5.aj_bv_agi_qk$6$(not in LMFDB)
4.5.af_t_aca_fe$6$(not in LMFDB)
4.5.ad_l_au_cc$6$(not in LMFDB)
4.5.b_h_ae_ba$6$(not in LMFDB)
4.5.d_l_u_cc$6$(not in LMFDB)
4.5.f_t_ca_fe$6$(not in LMFDB)
4.5.j_bv_gi_qk$6$(not in LMFDB)
4.5.ah_o_v_aew$8$(not in LMFDB)
4.5.ah_be_adn_is$8$(not in LMFDB)
4.5.af_i_p_ada$8$(not in LMFDB)
4.5.af_y_acn_gw$8$(not in LMFDB)
4.5.ab_ak_d_co$8$(not in LMFDB)
4.5.ab_ae_d_s$8$(not in LMFDB)
4.5.ab_g_an_bi$8$(not in LMFDB)
4.5.ab_m_an_de$8$(not in LMFDB)
4.5.b_ak_ad_co$8$(not in LMFDB)
4.5.b_ae_ad_s$8$(not in LMFDB)
4.5.b_g_n_bi$8$(not in LMFDB)
4.5.b_m_n_de$8$(not in LMFDB)
4.5.f_i_ap_ada$8$(not in LMFDB)
4.5.f_y_cn_gw$8$(not in LMFDB)
4.5.h_o_av_aew$8$(not in LMFDB)
4.5.h_be_dn_is$8$(not in LMFDB)
4.5.al_cj_aim_wa$12$(not in LMFDB)
4.5.aj_bj_ade_gm$12$(not in LMFDB)
4.5.ah_z_ack_fe$12$(not in LMFDB)
4.5.af_h_ba_aei$12$(not in LMFDB)
4.5.af_n_abc_cq$12$(not in LMFDB)
4.5.ad_ab_ak_cu$12$(not in LMFDB)
4.5.ad_f_aw_co$12$(not in LMFDB)
4.5.ad_f_ae_m$12$(not in LMFDB)
4.5.ad_f_e_am$12$(not in LMFDB)
4.5.ad_f_w_aco$12$(not in LMFDB)
4.5.ab_af_ac_bg$12$(not in LMFDB)
4.5.ab_b_ao_ba$12$(not in LMFDB)
4.5.b_af_c_bg$12$(not in LMFDB)
4.5.b_b_o_ba$12$(not in LMFDB)
4.5.d_ab_k_cu$12$(not in LMFDB)
4.5.d_f_aw_aco$12$(not in LMFDB)
4.5.d_f_ae_am$12$(not in LMFDB)
4.5.d_f_e_m$12$(not in LMFDB)
4.5.d_f_w_co$12$(not in LMFDB)
4.5.f_h_aba_aei$12$(not in LMFDB)
4.5.f_n_bc_cq$12$(not in LMFDB)
4.5.h_z_ck_fe$12$(not in LMFDB)
4.5.j_bj_de_gm$12$(not in LMFDB)
4.5.l_cj_im_wa$12$(not in LMFDB)