# Properties

 Label 4.5.al_ci_aih_vm 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: $( 1 - 4 x + 5 x^{2} )( 1 - 7 x + 27 x^{2} - 72 x^{3} + 135 x^{4} - 175 x^{5} + 125 x^{6} )$ Frobenius angles: $\pm0.0767028971338$, $\pm0.147583617650$, $\pm0.313688588913$, $\pm0.486729365003$ 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 $A(\F_{q^r})$ 68 368560 253973744 145725675520 95113205467828 60413486247562240 37408435140425549492 23303788858944706314240 14584444447485317147745776 9110344141423473374156090800

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ -5 25 130 597 3115 15838 78451 390973 1957486 9782145

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{5}$
 The isogeny class factors as 1.5.ae $\times$ 3.5.ah_bb_acu 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_b_as $2$ (not in LMFDB) 4.5.d_e_ab_as $2$ (not in LMFDB) 4.5.l_ci_ih_vm $2$ (not in LMFDB)
Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 4.5.ad_e_b_as $2$ (not in LMFDB) 4.5.d_e_ab_as $2$ (not in LMFDB) 4.5.l_ci_ih_vm $2$ (not in LMFDB) 4.5.aj_bu_agf_py $4$ (not in LMFDB) 4.5.af_s_acb_ew $4$ (not in LMFDB) 4.5.f_s_cb_ew $4$ (not in LMFDB) 4.5.j_bu_gf_py $4$ (not in LMFDB)