# Properties

 Label 4.5.am_ct_akj_bbk 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: $( 1 - 4 x + 5 x^{2} )( 1 - 8 x + 34 x^{2} - 93 x^{3} + 170 x^{4} - 200 x^{5} + 125 x^{6} )$ Frobenius angles: $\pm0.101435245160$, $\pm0.147583617650$, $\pm0.306436956418$, $\pm0.413672014132$ 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 $A(\F_{q^r})$ 58 365980 289808194 156569171840 94128265961138 59931647673780220 37696051384494647986 23438944479771914595840 14584359406912159084235392 9101614396243900551995791900

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ -6 24 147 640 3084 15711 79052 393232 1957476 9772784

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{5}$
 The isogeny class factors as 1.5.ae $\times$ 3.5.ai_bi_adp 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.ae_h_d_abg $2$ (not in LMFDB) 4.5.e_h_ad_abg $2$ (not in LMFDB) 4.5.m_ct_kj_bbk $2$ (not in LMFDB)
Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 4.5.ae_h_d_abg $2$ (not in LMFDB) 4.5.e_h_ad_abg $2$ (not in LMFDB) 4.5.m_ct_kj_bbk $2$ (not in LMFDB) 4.5.ak_cd_aht_ug $4$ (not in LMFDB) 4.5.ag_x_acn_fy $4$ (not in LMFDB) 4.5.g_x_cn_fy $4$ (not in LMFDB) 4.5.k_cd_ht_ug $4$ (not in LMFDB)