Properties

Label 4.5.an_de_aml_bhi
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:  $( 1 - 3 x + 5 x^{2} )( 1 - 2 x + 5 x^{2} )( 1 - 4 x + 5 x^{2} )^{2}$
Frobenius angles:  $\pm0.14758361765$, $\pm0.14758361765$, $\pm0.265942140215$, $\pm0.35241638235$
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
$A(\F_{q^r})$ 48 345600 317207808 176947200000 99339951101808 60212639880806400 37513870763864295408 23403120802607923200000 14584385684232990885973248 9098187204184464865659840000

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -7 21 158 717 3253 15786 78673 392637 1957478 9769101

Decomposition

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

Base change

This is a primitive isogeny class.