# Properties

 Label 4.5.al_ci_aii_vq 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: $( 1 - 4 x + 5 x^{2} )( 1 - 7 x + 27 x^{2} - 73 x^{3} + 135 x^{4} - 175 x^{5} + 125 x^{6} )$ Frobenius angles: $\pm0.0229621162481$, $\pm0.147583617650$, $\pm0.333082169302$, $\pm0.478604549684$ 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 $A(\F_{q^r})$ 66 358380 245992626 139189057920 91763628038346 59543280160366860 37270822609601606784 23256270099354103764480 14555004246562122843625026 9098524113569455041140805900

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ -5 25 127 569 3005 15613 78164 390177 1953541 9769465

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{5}$
 The isogeny class factors as 1.5.ae $\times$ 3.5.ah_bb_acv 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_e_a_aw $2$ (not in LMFDB) 4.5.d_e_a_aw $2$ (not in LMFDB) 4.5.l_ci_ii_vq $2$ (not in LMFDB)
Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 4.5.ad_e_a_aw $2$ (not in LMFDB) 4.5.d_e_a_aw $2$ (not in LMFDB) 4.5.l_ci_ii_vq $2$ (not in LMFDB) 4.5.aj_bu_agg_qa $4$ (not in LMFDB) 4.5.af_s_acc_eu $4$ (not in LMFDB) 4.5.f_s_cc_eu $4$ (not in LMFDB) 4.5.j_bu_gg_qa $4$ (not in LMFDB)