# Properties

 Label 4.5.al_ch_ahz_um 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: $( 1 - 4 x + 5 x^{2} )( 1 - 7 x + 26 x^{2} - 68 x^{3} + 130 x^{4} - 175 x^{5} + 125 x^{6} )$ Frobenius angles: $\pm0.0605820805461$, $\pm0.147583617650$, $\pm0.287119770935$, $\pm0.511693182811$ 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 $A(\F_{q^r})$ 64 340480 236305216 145954242560 97099396455424 60419585726456320 37120951071118044992 23226689054721740636160 14577807273559580351296576 9108081009512793909929574400

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ -5 23 121 599 3180 15839 77849 389679 1956595 9779718

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{5}$
 The isogeny class factors as 1.5.ae $\times$ 3.5.ah_ba_acq 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_d_b_am $2$ (not in LMFDB) 4.5.d_d_ab_am $2$ (not in LMFDB) 4.5.l_ch_hz_um $2$ (not in LMFDB)
Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 4.5.ad_d_b_am $2$ (not in LMFDB) 4.5.d_d_ab_am $2$ (not in LMFDB) 4.5.l_ch_hz_um $2$ (not in LMFDB) 4.5.aj_bt_afz_pg $4$ (not in LMFDB) 4.5.af_r_abz_eu $4$ (not in LMFDB) 4.5.f_r_bz_eu $4$ (not in LMFDB) 4.5.j_bt_fz_pg $4$ (not in LMFDB)