Properties

Label 4.5.ao_dn_any_blk
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:  $( 1 - 4 x + 5 x^{2} )^{2}( 1 - 6 x + 17 x^{2} - 30 x^{3} + 25 x^{4} )$
Frobenius angles:  $\pm0.0512862249088$, $\pm0.14758361765$, $\pm0.14758361765$, $\pm0.384619558242$
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
$A(\F_{q^r})$ 28 221200 230463856 148816281600 94313975316988 60307689652537600 37824215428924710268 23460952075775882035200 14573350564538393946716272 9090913800345378830015530000

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -8 12 118 608 3092 15810 79316 393600 1955998 9761292

Decomposition

1.5.ae 2 $\times$ 2.5.ag_r

Base change

This is a primitive isogeny class.