Properties

Label 4.5.an_df_ams_bie
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:  $( 1 - 4 x + 5 x^{2} )( 1 - 3 x + 5 x^{2} )^{3}$
Frobenius angles:  $\pm0.147583617650$, $\pm0.265942140215$, $\pm0.265942140215$, $\pm0.265942140215$
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
$A(\F_{q^r})$ 54 393660 364290048 196830000000 103259791417374 59657070843002880 36794213184728145438 23140362291178680000000 14542119714034827758444544 9103779873771429029456166300

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -7 23 176 787 3373 15638 77161 388227 1951808 9775103

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{5}$
The isogeny class factors as 1.5.ae $\times$ 1.5.ad 3 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.ah_x_abq_cu$2$(not in LMFDB)
4.5.af_l_g_abw$2$(not in LMFDB)
4.5.ab_ab_ag_bw$2$(not in LMFDB)
4.5.b_ab_g_bw$2$(not in LMFDB)
4.5.f_l_ag_abw$2$(not in LMFDB)
4.5.h_x_bq_cu$2$(not in LMFDB)
4.5.n_df_ms_bie$2$(not in LMFDB)
4.5.ae_f_s_acu$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
4.5.ah_x_abq_cu$2$(not in LMFDB)
4.5.af_l_g_abw$2$(not in LMFDB)
4.5.ab_ab_ag_bw$2$(not in LMFDB)
4.5.b_ab_g_bw$2$(not in LMFDB)
4.5.f_l_ag_abw$2$(not in LMFDB)
4.5.h_x_bq_cu$2$(not in LMFDB)
4.5.n_df_ms_bie$2$(not in LMFDB)
4.5.ae_f_s_acu$3$(not in LMFDB)
4.5.al_cn_ajm_ze$4$(not in LMFDB)
4.5.ah_v_abc_bc$4$(not in LMFDB)
4.5.ah_bd_ada_he$4$(not in LMFDB)
4.5.af_p_au_bi$4$(not in LMFDB)
4.5.af_r_abe_co$4$(not in LMFDB)
4.5.ab_ad_ae_ca$4$(not in LMFDB)
4.5.ab_d_ae_bu$4$(not in LMFDB)
4.5.ab_f_ag_cc$4$(not in LMFDB)
4.5.b_ad_e_ca$4$(not in LMFDB)
4.5.b_d_e_bu$4$(not in LMFDB)
4.5.b_f_g_cc$4$(not in LMFDB)
4.5.f_p_u_bi$4$(not in LMFDB)
4.5.f_r_be_co$4$(not in LMFDB)
4.5.h_v_bc_bc$4$(not in LMFDB)
4.5.h_bd_da_he$4$(not in LMFDB)
4.5.l_cn_jm_ze$4$(not in LMFDB)
4.5.ak_bv_afo_nk$6$(not in LMFDB)
4.5.ae_f_as_cu$6$(not in LMFDB)
4.5.ac_ab_a_m$6$(not in LMFDB)
4.5.c_ab_a_m$6$(not in LMFDB)
4.5.e_f_as_acu$6$(not in LMFDB)
4.5.e_f_s_cu$6$(not in LMFDB)
4.5.k_bv_fo_nk$6$(not in LMFDB)
4.5.ai_bj_aee_ke$12$(not in LMFDB)
4.5.ae_l_abk_ds$12$(not in LMFDB)
4.5.ac_f_as_bk$12$(not in LMFDB)
4.5.ac_f_s_abk$12$(not in LMFDB)
4.5.c_f_as_abk$12$(not in LMFDB)
4.5.c_f_s_bk$12$(not in LMFDB)
4.5.e_l_bk_ds$12$(not in LMFDB)
4.5.i_bj_ee_ke$12$(not in LMFDB)