Properties

Label 4.5.al_ci_aif_ve
Base Field $\F_{5}$
Dimension $4$
$p$-rank $3$
Does not contain a Jacobian

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Invariants

Base field:  $\F_{5}$
Dimension:  $4$
Weil polynomial:  $( 1 - 3 x + 5 x^{2} )( 1 + 5 x^{2} )( 1 - 4 x + 5 x^{2} )^{2}$
Frobenius angles:  $\pm0.14758361765$, $\pm0.14758361765$, $\pm0.265942140215$, $\pm0.5$
Angle rank:  $2$ (numerical)

Newton polygon

$p$-rank:  $3$
Slopes:  $[0, 0, 0, 1/2, 1/2, 1, 1, 1]$

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
$A(\F_{q^r})$ 72 388800 270055296 159252480000 102015994462632 62106020708659200 37541741395932545256 23265455386121994240000 14566501292698654967751552 9104451951600678800860920000

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -5 25 136 653 3335 16270 78731 390333 1955080 9775825

Decomposition

1.5.ae 2 $\times$ 1.5.ad $\times$ 1.5.a

Base change

This is a primitive isogeny class.