# Properties

 Label 4.5.am_cp_ajc_xg 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: $( 1 - 4 x + 5 x^{2} )^{2}( 1 - 4 x + 9 x^{2} - 20 x^{3} + 25 x^{4} )$ Frobenius angles: $\pm0.103885594917$, $\pm0.147583617650$, $\pm0.147583617650$, $\pm0.516810247272$ 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 $A(\F_{q^r})$ 44 259600 206947136 144877568000 101344979199244 62729484748902400 37865824253945399756 23405215805135290368000 14603329963432731221966144 9106643109419934768670090000

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ -6 16 102 592 3314 16426 79402 392672 1960014 9778176

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{5}$
 The isogeny class factors as 1.5.ae 2 $\times$ 2.5.ae_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.ae_j : 4.0.1025.1.
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.ae_d_e_ae $2$ (not in LMFDB) 4.5.ae_d_m_abk $2$ (not in LMFDB) 4.5.e_d_am_abk $2$ (not in LMFDB) 4.5.e_d_ae_ae $2$ (not in LMFDB) 4.5.m_cp_jc_xg $2$ (not in LMFDB) 4.5.a_e_ai_al $3$ (not in LMFDB)
Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 4.5.ae_d_e_ae $2$ (not in LMFDB) 4.5.ae_d_m_abk $2$ (not in LMFDB) 4.5.e_d_am_abk $2$ (not in LMFDB) 4.5.e_d_ae_ae $2$ (not in LMFDB) 4.5.m_cp_jc_xg $2$ (not in LMFDB) 4.5.a_e_ai_al $3$ (not in LMFDB) 4.5.ak_bz_agu_rk $4$ (not in LMFDB) 4.5.ai_bn_afc_my $4$ (not in LMFDB) 4.5.ag_t_ace_fs $4$ (not in LMFDB) 4.5.ae_p_abs_ea $4$ (not in LMFDB) 4.5.ac_d_a_am $4$ (not in LMFDB) 4.5.ac_d_i_abc $4$ (not in LMFDB) 4.5.a_h_au_q $4$ (not in LMFDB) 4.5.a_h_u_q $4$ (not in LMFDB) 4.5.c_d_ai_abc $4$ (not in LMFDB) 4.5.c_d_a_am $4$ (not in LMFDB) 4.5.e_p_bs_ea $4$ (not in LMFDB) 4.5.g_t_ce_fs $4$ (not in LMFDB) 4.5.i_bn_fc_my $4$ (not in LMFDB) 4.5.k_bz_gu_rk $4$ (not in LMFDB) 4.5.ai_bk_aeq_lx $6$ (not in LMFDB) 4.5.a_e_i_al $6$ (not in LMFDB) 4.5.i_bk_eq_lx $6$ (not in LMFDB) 4.5.ae_b_m_aw $8$ (not in LMFDB) 4.5.ae_r_aca_es $8$ (not in LMFDB) 4.5.e_b_am_aw $8$ (not in LMFDB) 4.5.e_r_ca_es $8$ (not in LMFDB) 4.5.ag_q_abs_er $12$ (not in LMFDB) 4.5.ac_a_m_abn $12$ (not in LMFDB) 4.5.c_a_am_abn $12$ (not in LMFDB) 4.5.g_q_bs_er $12$ (not in LMFDB)