# 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

## 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.

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 52 254800 188267716 152635392000 104445396370432 61894084760981200 37743422774763944836 23522449559682318336000 14607820454067422008883092 9095901361683172330577920000

 $r$ 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: 1.5.ae 2 : $\mathrm{M}_{2}($$$\Q(\sqrt{-1})$$$)$ 2.5.ad_f : 4.0.37845.1.
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.
 Twist Extension Degree Common 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.
 Twist Extension Degree Common 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)