Properties

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

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Invariants

Base field:  $\F_{5}$
Dimension:  $4$
Weil polynomial:  $( 1 - 4 x + 5 x^{2} )^{2}( 1 - 4 x + 8 x^{2} - 20 x^{3} + 25 x^{4} )$
Frobenius angles:  $\pm0.0320471084245$, $\pm0.14758361765$, $\pm0.14758361765$, $\pm0.532047108424$
Angle rank:  $2$ (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.

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 40 232000 185901160 137789440000 98724762356200 61408246839784000 37406785762368758440 23305441008408330240000 14576888205733196794245160 9095832593830975111969000000

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -6 14 90 562 3234 16094 78450 391002 1956474 9766574

Decomposition

1.5.ae 2 $\times$ 2.5.ae_i

Base change

This is a primitive isogeny class.