Properties

Label 4.5.ap_ea_aqr_btm
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:  $( 1 - 3 x + 5 x^{2} )( 1 - 4 x + 5 x^{2} )^{3}$
Frobenius angles:  $\pm0.14758361765$, $\pm0.14758361765$, $\pm0.14758361765$, $\pm0.265942140215$
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
$A(\F_{q^r})$ 24 216000 261482112 176947200000 104496229772664 62043429606912000 37808915041276457592 23403120802607923200000 14577211045093695158980224 9099070455307393302687000000

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -9 9 132 717 3411 16254 79287 392637 1956516 9770049

Decomposition

1.5.ae 3 $\times$ 1.5.ad

Base change

This is a primitive isogeny class.