Properties

Label 4.5.am_ct_aki_bbg
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:  $( 1 - 3 x + 5 x^{2} )( 1 - x + 5 x^{2} )( 1 - 4 x + 5 x^{2} )^{2}$
Frobenius angles:  $\pm0.14758361765$, $\pm0.14758361765$, $\pm0.265942140215$, $\pm0.428216853436$
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
$A(\F_{q^r})$ 60 378000 300061440 164505600000 98719892274300 61339279712256000 37810356625693780860 23357411582290329600000 14547811432321238032362240 9094947685034230503272250000

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -6 24 150 672 3234 16074 79290 391872 1952574 9765624

Decomposition

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

Base change

This is a primitive isogeny class.