Properties

Label 4.5.aq_em_atc_cao
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:  $( 1 - 4 x + 5 x^{2} )^{4}$
Frobenius angles:  $\pm0.14758361765$, $\pm0.14758361765$, $\pm0.14758361765$, $\pm0.14758361765$
Angle rank:  $1$ (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
$A(\F_{q^r})$ 16 160000 221533456 167772160000 105119989862416 63272170368160000 38326711929781551376 23535616807151861760000 14594788452214325009080336 9096716659728898824100000000

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -10 2 110 682 3430 16562 80350 394842 1958870 9767522

Decomposition

1.5.ae 4

Base change

This is a primitive isogeny class.