# Properties

 Label 4.5.am_cs_akb_bak 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: $( 1 - 4 x + 5 x^{2} )( 1 - 3 x + 5 x^{2} )( 1 - 5 x + 13 x^{2} - 25 x^{3} + 25 x^{4} )$ Frobenius angles: $\pm0.0878807261908$, $\pm0.147583617650$, $\pm0.265942140215$, $\pm0.450170915301$ Angle rank: $4$ (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 $A(\F_{q^r})$ 54 335340 265153824 152646768000 96425619575904 60878289193562880 37608663565748948454 23298326743389451200000 14551714461451081885255584 9103624378553472574290739200

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ -6 22 135 626 3159 15955 78870 390882 1953099 9774937

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{5}$
 The isogeny class factors as 1.5.ae $\times$ 1.5.ad $\times$ 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:
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.ag_q_abh_cw $2$ (not in LMFDB) 4.5.ae_g_d_aba $2$ (not in LMFDB) 4.5.ac_a_j_ao $2$ (not in LMFDB) 4.5.c_a_aj_ao $2$ (not in LMFDB) 4.5.e_g_ad_aba $2$ (not in LMFDB) 4.5.g_q_bh_cw $2$ (not in LMFDB) 4.5.m_cs_kb_bak $2$ (not in LMFDB)
Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 4.5.ag_q_abh_cw $2$ (not in LMFDB) 4.5.ae_g_d_aba $2$ (not in LMFDB) 4.5.ac_a_j_ao $2$ (not in LMFDB) 4.5.c_a_aj_ao $2$ (not in LMFDB) 4.5.e_g_ad_aba $2$ (not in LMFDB) 4.5.g_q_bh_cw $2$ (not in LMFDB) 4.5.m_cs_kb_bak $2$ (not in LMFDB) 4.5.ak_cc_ahn_to $4$ (not in LMFDB) 4.5.ag_w_acl_fw $4$ (not in LMFDB) 4.5.ae_m_abb_ca $4$ (not in LMFDB) 4.5.a_e_ap_i $4$ (not in LMFDB) 4.5.a_e_p_i $4$ (not in LMFDB) 4.5.e_m_bb_ca $4$ (not in LMFDB) 4.5.g_w_cl_fw $4$ (not in LMFDB) 4.5.k_cc_hn_to $4$ (not in LMFDB)