# Properties

 Label 4.5.al_cg_ahq_ti 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: $( 1 - 4 x + 5 x^{2} )( 1 - 7 x + 25 x^{2} - 63 x^{3} + 125 x^{4} - 175 x^{5} + 125 x^{6} )$ Frobenius angles: $\pm0.0923731703714$, $\pm0.147583617650$, $\pm0.243942915084$, $\pm0.536165446792$ 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 $A(\F_{q^r})$ 62 323020 227332238 152331063680 102004742170342 61542658281520780 37284327213404217344 23277220076463368394240 14581361287667006692266974 9102397551739387088407677100

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ -5 21 115 625 3335 16125 78192 390529 1957075 9773621

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{5}$
 The isogeny class factors as 1.5.ae $\times$ 3.5.ah_z_acl 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.ad_c_c_ac $2$ (not in LMFDB) 4.5.d_c_ac_ac $2$ (not in LMFDB) 4.5.l_cg_hq_ti $2$ (not in LMFDB)
Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 4.5.ad_c_c_ac $2$ (not in LMFDB) 4.5.d_c_ac_ac $2$ (not in LMFDB) 4.5.l_cg_hq_ti $2$ (not in LMFDB) 4.5.aj_bs_afs_om $4$ (not in LMFDB) 4.5.af_q_abw_eu $4$ (not in LMFDB) 4.5.f_q_bw_eu $4$ (not in LMFDB) 4.5.j_bs_fs_om $4$ (not in LMFDB)