Properties

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

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Invariants

Base field:  $\F_{5}$
Dimension:  $4$
L-polynomial:  $( 1 - 4 x + 5 x^{2} )^{2}( 1 - 3 x + 8 x^{2} - 15 x^{3} + 25 x^{4} )$
Frobenius angles:  $\pm0.147583617650$, $\pm0.147583617650$, $\pm0.206741677780$, $\pm0.540075011113$
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
$A(\F_{q^r})$ 64 332800 235286272 159488409600 105937056318784 62857951053414400 37622750928200078656 23334330333320655667200 14573326513210221066708736 9091927125274661971438720000

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -5 21 118 653 3455 16458 78899 391485 1955998 9762381

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{5}$
The isogeny class factors as 1.5.ae 2 $\times$ 2.5.ad_i 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.ha 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.ad_c_d_c$2$(not in LMFDB)
4.5.d_c_ad_c$2$(not in LMFDB)
4.5.f_k_l_s$2$(not in LMFDB)
4.5.l_cg_hp_te$2$(not in LMFDB)
4.5.ai_t_q_afc$3$(not in LMFDB)
4.5.af_k_al_s$3$(not in LMFDB)
4.5.b_h_e_s$3$(not in LMFDB)
4.5.e_e_ai_abb$3$(not in LMFDB)
4.5.h_bf_dw_jy$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
4.5.ad_c_d_c$2$(not in LMFDB)
4.5.d_c_ad_c$2$(not in LMFDB)
4.5.f_k_l_s$2$(not in LMFDB)
4.5.l_cg_hp_te$2$(not in LMFDB)
4.5.ai_t_q_afc$3$(not in LMFDB)
4.5.af_k_al_s$3$(not in LMFDB)
4.5.b_h_e_s$3$(not in LMFDB)
4.5.e_e_ai_abb$3$(not in LMFDB)
4.5.h_bf_dw_jy$3$(not in LMFDB)
4.5.aj_bs_afr_ok$4$(not in LMFDB)
4.5.ah_bi_aef_kw$4$(not in LMFDB)
4.5.af_q_abv_ew$4$(not in LMFDB)
4.5.ad_i_aj_o$4$(not in LMFDB)
4.5.ad_o_abh_du$4$(not in LMFDB)
4.5.ab_e_f_g$4$(not in LMFDB)
4.5.ab_k_f_bq$4$(not in LMFDB)
4.5.b_e_af_g$4$(not in LMFDB)
4.5.b_k_af_bq$4$(not in LMFDB)
4.5.d_i_j_o$4$(not in LMFDB)
4.5.d_o_bh_du$4$(not in LMFDB)
4.5.f_q_bv_ew$4$(not in LMFDB)
4.5.h_bi_ef_kw$4$(not in LMFDB)
4.5.j_bs_fr_ok$4$(not in LMFDB)
4.5.ah_bf_adw_jy$6$(not in LMFDB)
4.5.ae_e_i_abb$6$(not in LMFDB)
4.5.ab_h_ae_s$6$(not in LMFDB)
4.5.a_an_a_do$6$(not in LMFDB)
4.5.i_t_aq_afc$6$(not in LMFDB)
4.5.ad_a_j_ao$8$(not in LMFDB)
4.5.ad_q_abn_ek$8$(not in LMFDB)
4.5.d_a_aj_ao$8$(not in LMFDB)
4.5.d_q_bn_ek$8$(not in LMFDB)
4.5.ai_bh_ads_iy$12$(not in LMFDB)
4.5.ag_l_m_acy$12$(not in LMFDB)
4.5.ag_z_acu_gu$12$(not in LMFDB)
4.5.af_n_abm_dy$12$(not in LMFDB)
4.5.ae_h_i_abw$12$(not in LMFDB)
4.5.ae_s_abw_ex$12$(not in LMFDB)
4.5.ae_v_abw_fs$12$(not in LMFDB)
4.5.ac_ai_e_cf$12$(not in LMFDB)
4.5.ac_af_e_bk$12$(not in LMFDB)
4.5.ac_g_ay_br$12$(not in LMFDB)
4.5.ac_j_ay_cm$12$(not in LMFDB)
4.5.ab_b_o_as$12$(not in LMFDB)
4.5.a_ab_a_i$12$(not in LMFDB)
4.5.a_b_a_i$12$(not in LMFDB)
4.5.a_n_a_do$12$(not in LMFDB)
4.5.b_b_ao_as$12$(not in LMFDB)
4.5.c_ai_ae_cf$12$(not in LMFDB)
4.5.c_af_ae_bk$12$(not in LMFDB)
4.5.c_g_y_br$12$(not in LMFDB)
4.5.c_j_y_cm$12$(not in LMFDB)
4.5.e_h_ai_abw$12$(not in LMFDB)
4.5.e_s_bw_ex$12$(not in LMFDB)
4.5.e_v_bw_fs$12$(not in LMFDB)
4.5.f_n_bm_dy$12$(not in LMFDB)
4.5.g_l_am_acy$12$(not in LMFDB)
4.5.g_z_cu_gu$12$(not in LMFDB)
4.5.i_bh_ds_iy$12$(not in LMFDB)
4.5.a_ap_a_ec$24$(not in LMFDB)
4.5.a_ab_a_ag$24$(not in LMFDB)
4.5.a_b_a_ag$24$(not in LMFDB)
4.5.a_p_a_ec$24$(not in LMFDB)