Properties

Label 4.5.al_cd_agr_qe
Base Field $\F_{5}$
Dimension $4$
Ordinary No
$p$-rank $3$
Principally polarizable Yes
Contains a Jacobian No

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Invariants

Base field:  $\F_{5}$
Dimension:  $4$
L-polynomial:  $( 1 - 4 x + 5 x^{2} )^{2}( 1 - 3 x + 5 x^{2} - 15 x^{3} + 25 x^{4} )$
Frobenius angles:  $\pm0.113143297209$, $\pm0.147583617650$, $\pm0.147583617650$, $\pm0.585923223955$
Angle rank:  $3$ (numerical)

This isogeny class is not simple.

Newton polygon

$p$-rank:  $3$
Slopes:  $[0, 0, 0, 1/2, 1/2, 1, 1, 1]$

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
$A(\F_{q^r})$ 52 254800 188267716 152635392000 104445396370432 61894084760981200 37743422774763944836 23522449559682318336000 14607820454067422008883092 9095901361683172330577920000

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -5 15 91 623 3410 16215 79151 394623 1960615 9766650

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{5}$
The isogeny class factors as 1.5.ae 2 $\times$ 2.5.ad_f 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.af_h_n_aci$2$(not in LMFDB)
4.5.ad_ab_d_u$2$(not in LMFDB)
4.5.d_ab_ad_u$2$(not in LMFDB)
4.5.f_h_an_aci$2$(not in LMFDB)
4.5.l_cd_gr_qe$2$(not in LMFDB)
4.5.b_e_ai_ap$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
4.5.af_h_n_aci$2$(not in LMFDB)
4.5.ad_ab_d_u$2$(not in LMFDB)
4.5.d_ab_ad_u$2$(not in LMFDB)
4.5.f_h_an_aci$2$(not in LMFDB)
4.5.l_cd_gr_qe$2$(not in LMFDB)
4.5.b_e_ai_ap$3$(not in LMFDB)
4.5.aj_bp_aez_mi$4$(not in LMFDB)
4.5.ah_bf_adt_jg$4$(not in LMFDB)
4.5.af_n_abp_eq$4$(not in LMFDB)
4.5.ad_f_j_abo$4$(not in LMFDB)
4.5.ad_l_abh_dc$4$(not in LMFDB)
4.5.ab_b_ab_a$4$(not in LMFDB)
4.5.ab_h_r_a$4$(not in LMFDB)
4.5.b_b_b_a$4$(not in LMFDB)
4.5.b_h_ar_a$4$(not in LMFDB)
4.5.d_f_aj_abo$4$(not in LMFDB)
4.5.d_l_bh_dc$4$(not in LMFDB)
4.5.f_n_bp_eq$4$(not in LMFDB)
4.5.h_bf_dt_jg$4$(not in LMFDB)
4.5.j_bp_ez_mi$4$(not in LMFDB)
4.5.ah_bc_adk_ir$6$(not in LMFDB)
4.5.ab_e_i_ap$6$(not in LMFDB)
4.5.h_bc_dk_ir$6$(not in LMFDB)
4.5.ad_ad_j_k$8$(not in LMFDB)
4.5.ad_n_abn_dm$8$(not in LMFDB)
4.5.d_ad_aj_k$8$(not in LMFDB)
4.5.d_n_bn_dm$8$(not in LMFDB)
4.5.af_k_abg_eb$12$(not in LMFDB)
4.5.ab_ac_i_ap$12$(not in LMFDB)
4.5.b_ac_ai_ap$12$(not in LMFDB)
4.5.f_k_bg_eb$12$(not in LMFDB)