Properties

Label 4.5.am_cs_aka_bag
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:  $( 1 - 4 x + 5 x^{2} )^{2}( 1 - 4 x + 12 x^{2} - 20 x^{3} + 25 x^{4} )$
Frobenius angles:  $\pm0.14758361765$, $\pm0.14758361765$, $\pm0.223508181938$, $\pm0.458185759261$
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.

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 56 347200 275264696 160700825600 101269959432376 62587649617729600 37947228001422018104 23313090284952433459200 14533235451611243981663672 9093008912788201114938280000

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -6 22 138 658 3314 16390 79570 391130 1950618 9763542

Decomposition

1.5.ae 2 $\times$ 2.5.ae_m

Base change

This is a primitive isogeny class.