Properties

Label 4.5.al_cj_aip_wm
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:  $( 1 - 4 x + 5 x^{2} )( 1 - 2 x + 5 x^{2} )( 1 - 5 x + 13 x^{2} - 25 x^{3} + 25 x^{4} )$
Frobenius angles:  $\pm0.0878807261908$, $\pm0.147583617650$, $\pm0.352416382350$, $\pm0.450170915301$
Angle rank:  $3$ (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
$A(\F_{q^r})$ 72 397440 272519208 144731750400 92214761542272 60251969345892480 37826217127905395688 23430229459787612160000 14576431850763169422818952 9100385940366051423171379200

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -5 27 139 591 3020 15795 79319 393087 1956415 9771462

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{5}$
The isogeny class factors as 1.5.ae $\times$ 1.5.ac $\times$ 2.5.af_n 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 2 $\times$ 2.625.acl_dfd. 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.ah_z_act_gu$2$(not in LMFDB)
4.5.ad_f_b_ay$2$(not in LMFDB)
4.5.ab_b_h_aq$2$(not in LMFDB)
4.5.b_b_ah_aq$2$(not in LMFDB)
4.5.d_f_ab_ay$2$(not in LMFDB)
4.5.h_z_ct_gu$2$(not in LMFDB)
4.5.l_cj_ip_wm$2$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
4.5.ah_z_act_gu$2$(not in LMFDB)
4.5.ad_f_b_ay$2$(not in LMFDB)
4.5.ab_b_h_aq$2$(not in LMFDB)
4.5.b_b_ah_aq$2$(not in LMFDB)
4.5.d_f_ab_ay$2$(not in LMFDB)
4.5.h_z_ct_gu$2$(not in LMFDB)
4.5.l_cj_ip_wm$2$(not in LMFDB)
4.5.an_db_aln_bei$4$(not in LMFDB)
4.5.aj_bv_agl_qq$4$(not in LMFDB)
4.5.af_h_f_abc$4$(not in LMFDB)
4.5.af_t_acd_ey$4$(not in LMFDB)
4.5.ad_ab_l_am$4$(not in LMFDB)
4.5.ab_h_ax_bg$4$(not in LMFDB)
4.5.b_h_x_bg$4$(not in LMFDB)
4.5.d_ab_al_am$4$(not in LMFDB)
4.5.f_h_af_abc$4$(not in LMFDB)
4.5.f_t_cd_ey$4$(not in LMFDB)
4.5.j_bv_gl_qq$4$(not in LMFDB)
4.5.n_db_ln_bei$4$(not in LMFDB)
4.5.af_f_p_acc$8$(not in LMFDB)
4.5.af_v_acn_fy$8$(not in LMFDB)
4.5.f_f_ap_acc$8$(not in LMFDB)
4.5.f_v_cn_fy$8$(not in LMFDB)
4.5.aj_bs_afw_pd$12$(not in LMFDB)
4.5.ah_w_ace_fh$12$(not in LMFDB)
4.5.ad_c_q_acl$12$(not in LMFDB)
4.5.ab_e_ai_ah$12$(not in LMFDB)
4.5.b_e_i_ah$12$(not in LMFDB)
4.5.d_c_aq_acl$12$(not in LMFDB)
4.5.h_w_ce_fh$12$(not in LMFDB)
4.5.j_bs_fw_pd$12$(not in LMFDB)