# Properties

 Label 4.5.al_cf_ahi_si 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: $( 1 - 4 x + 5 x^{2} )( 1 - 7 x + 24 x^{2} - 59 x^{3} + 120 x^{4} - 175 x^{5} + 125 x^{6} )$ Frobenius angles: $\pm0.0749012311065$, $\pm0.147583617650$, $\pm0.225515375241$, $\pm0.553262127050$ 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 296380 211105384 150921438080 102289949299058 61311750441672640 37227732300849261922 23290811307029403164160 14573500322886707436902248 9094849235129799353382307900

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ -5 19 106 619 3345 16066 78073 390755 1956022 9765519

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{5}$
 The isogeny class factors as 1.5.ae $\times$ 3.5.ah_y_ach 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_b_c_e $2$ (not in LMFDB) 4.5.d_b_ac_e $2$ (not in LMFDB) 4.5.l_cf_hi_si $2$ (not in LMFDB)
Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 4.5.ad_b_c_e $2$ (not in LMFDB) 4.5.d_b_ac_e $2$ (not in LMFDB) 4.5.l_cf_hi_si $2$ (not in LMFDB) 4.5.aj_br_afm_nu $4$ (not in LMFDB) 4.5.af_p_abu_es $4$ (not in LMFDB) 4.5.f_p_bu_es $4$ (not in LMFDB) 4.5.j_br_fm_nu $4$ (not in LMFDB)