Properties

Label 4.5.an_db_aln_bei
Base field $\F_{5}$
Dimension $4$
$p$-rank $4$
Ordinary yes
Supersingular no
Simple no
Geometrically simple no
Primitive yes
Principally polarizable yes
Contains a Jacobian no

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Invariants

Base field:  $\F_{5}$
Dimension:  $4$
L-polynomial:  $( 1 - 4 x + 5 x^{2} )^{2}( 1 - 5 x + 13 x^{2} - 25 x^{3} + 25 x^{4} )$
  $1 - 13 x + 79 x^{2} - 299 x^{3} + 788 x^{4} - 1495 x^{5} + 1975 x^{6} - 1625 x^{7} + 625 x^{8}$
Frobenius angles:  $\pm0.0878807261908$, $\pm0.147583617650$, $\pm0.147583617650$, $\pm0.450170915301$
Angle rank:  $3$ (numerical)

This isogeny class is not simple, primitive, ordinary, and not supersingular. It is principally polarizable.

Newton polygon

This isogeny class is ordinary.

$p$-rank:  $4$
Slopes:  $[0, 0, 0, 0, 1, 1, 1, 1]$

Point counts

Point counts of the abelian variety

$r$ $1$ $2$ $3$ $4$ $5$
$A(\F_{q^r})$ $36$ $248400$ $224644212$ $144731750400$ $97001204486976$

Point counts of the (virtual) curve

$r$ $1$ $2$ $3$ $4$ $5$ $6$ $7$ $8$ $9$ $10$
$C(\F_{q^r})$ $-7$ $15$ $113$ $591$ $3178$ $16263$ $79933$ $393087$ $1955453$ $9772410$

Jacobians and polarizations

This isogeny class is principally polarizable, but does not contain a Jacobian.

Decomposition and endomorphism algebra

All geometric endomorphisms are defined over $\F_{5}$.

Endomorphism algebra over $\F_{5}$
The isogeny class factors as 1.5.ae 2 $\times$ 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:

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.af_h_f_abc$2$(not in LMFDB)
4.5.ad_ab_l_am$2$(not in LMFDB)
4.5.d_ab_al_am$2$(not in LMFDB)
4.5.f_h_af_abc$2$(not in LMFDB)
4.5.n_db_ln_bei$2$(not in LMFDB)
4.5.ab_e_ai_ah$3$(not in LMFDB)

Below is a list of all twists of this isogeny class.

TwistExtension degreeCommon base change
4.5.af_h_f_abc$2$(not in LMFDB)
4.5.ad_ab_l_am$2$(not in LMFDB)
4.5.d_ab_al_am$2$(not in LMFDB)
4.5.f_h_af_abc$2$(not in LMFDB)
4.5.n_db_ln_bei$2$(not in LMFDB)
4.5.ab_e_ai_ah$3$(not in LMFDB)
4.5.al_cj_aip_wm$4$(not in LMFDB)
4.5.aj_bv_agl_qq$4$(not in LMFDB)
4.5.ah_z_act_gu$4$(not in LMFDB)
4.5.af_t_acd_ey$4$(not in LMFDB)
4.5.ad_f_b_ay$4$(not in LMFDB)
4.5.ab_b_h_aq$4$(not in LMFDB)
4.5.ab_h_ax_bg$4$(not in LMFDB)
4.5.b_b_ah_aq$4$(not in LMFDB)
4.5.b_h_x_bg$4$(not in LMFDB)
4.5.d_f_ab_ay$4$(not in LMFDB)
4.5.f_t_cd_ey$4$(not in LMFDB)
4.5.h_z_ct_gu$4$(not in LMFDB)
4.5.j_bv_gl_qq$4$(not in LMFDB)
4.5.l_cj_ip_wm$4$(not in LMFDB)
4.5.aj_bs_afw_pd$6$(not in LMFDB)
4.5.b_e_i_ah$6$(not in LMFDB)
4.5.j_bs_fw_pd$6$(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.ah_w_ace_fh$12$(not in LMFDB)
4.5.ad_c_q_acl$12$(not in LMFDB)
4.5.d_c_aq_acl$12$(not in LMFDB)
4.5.h_w_ce_fh$12$(not in LMFDB)