# Properties

 Label 4.5.al_cf_ahh_se Base Field $\F_{5}$ Dimension $4$ $p$-rank $4$ Does not contain a Jacobian

## Invariants

 Base field: $\F_{5}$ Dimension: $4$ Weil polynomial: $( 1 - 4 x + 5 x^{2} )^{2}( 1 - 3 x + 7 x^{2} - 15 x^{3} + 25 x^{4} )$ Frobenius angles: $\pm0.14758361765$, $\pm0.14758361765$, $\pm0.177952114464$, $\pm0.556618995437$ Angle rank: $3$ (numerical)

## Newton polygon

This isogeny class is ordinary.

 $p$-rank: $4$ Slopes: $[0, 0, 0, 0, 1, 1, 1, 1]$

## Point counts

This isogeny class does not contain a Jacobian, and it is unknown whether it is principally polarizable.

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 60 306000 219018060 158238720000 106436408884800 62860964749362000 37723253866119092940 23415883237073387520000 14587645433752853450921340 9090152629464840455232000000

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ -5 19 109 647 3470 16459 79109 392847 1957915 9760474

## Decomposition

1.5.ae 2 $\times$ 2.5.ad_h

## Base change

This is a primitive isogeny class.