# Properties

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

## Invariants

 Base field: $\F_{5}$ Dimension: $4$ L-polynomial: $( 1 - 4 x + 5 x^{2} )^{2}( 1 - 3 x + 9 x^{2} - 15 x^{3} + 25 x^{4} )$ Frobenius angles: $\pm0.147583617650$, $\pm0.147583617650$, $\pm0.235523574971$, $\pm0.521566933142$ 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.

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 68 360400 252268916 159798476800 104455895241728 62590163252952400 37542139214220476372 23275134774468653875200 14565881008837190764198724 9097810705223061110824960000

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ -5 23 127 655 3410 16391 78731 390495 1954999 9768698

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{5}$
 The isogeny class factors as 1.5.ae 2 $\times$ 2.5.ad_j 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_j : 4.0.30589.1.
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_l_at_bs $2$ (not in LMFDB) 4.5.ad_d_d_ae $2$ (not in LMFDB) 4.5.d_d_ad_ae $2$ (not in LMFDB) 4.5.f_l_t_bs $2$ (not in LMFDB) 4.5.l_ch_hx_ue $2$ (not in LMFDB) 4.5.b_i_i_bd $3$ (not in LMFDB)
Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 4.5.af_l_at_bs $2$ (not in LMFDB) 4.5.ad_d_d_ae $2$ (not in LMFDB) 4.5.d_d_ad_ae $2$ (not in LMFDB) 4.5.f_l_t_bs $2$ (not in LMFDB) 4.5.l_ch_hx_ue $2$ (not in LMFDB) 4.5.b_i_i_bd $3$ (not in LMFDB) 4.5.aj_bt_afx_pc $4$ (not in LMFDB) 4.5.ah_bj_aej_lk $4$ (not in LMFDB) 4.5.af_r_abx_ey $4$ (not in LMFDB) 4.5.ad_j_ap_bg $4$ (not in LMFDB) 4.5.ad_p_abh_ea $4$ (not in LMFDB) 4.5.ab_f_h_i $4$ (not in LMFDB) 4.5.ab_l_b_ce $4$ (not in LMFDB) 4.5.b_f_ah_i $4$ (not in LMFDB) 4.5.b_l_ab_ce $4$ (not in LMFDB) 4.5.d_j_p_bg $4$ (not in LMFDB) 4.5.d_p_bh_ea $4$ (not in LMFDB) 4.5.f_r_bx_ey $4$ (not in LMFDB) 4.5.h_bj_ej_lk $4$ (not in LMFDB) 4.5.j_bt_fx_pc $4$ (not in LMFDB) 4.5.ah_bg_aea_kj $6$ (not in LMFDB) 4.5.ab_i_ai_bd $6$ (not in LMFDB) 4.5.h_bg_ea_kj $6$ (not in LMFDB) 4.5.ad_b_j_aw $8$ (not in LMFDB) 4.5.ad_r_abn_es $8$ (not in LMFDB) 4.5.d_b_aj_aw $8$ (not in LMFDB) 4.5.d_r_bn_es $8$ (not in LMFDB) 4.5.af_o_abo_dx $12$ (not in LMFDB) 4.5.ab_c_q_at $12$ (not in LMFDB) 4.5.b_c_aq_at $12$ (not in LMFDB) 4.5.f_o_bo_dx $12$ (not in LMFDB)