Properties

Label 4.5.am_cw_alc_bdr
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:  $( 1 - 3 x + 5 x^{2} )^{4}$
Frobenius angles:  $\pm0.265942140215$, $\pm0.265942140215$, $\pm0.265942140215$, $\pm0.265942140215$
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
$A(\F_{q^r})$ 81 531441 429981696 207594140625 102647069357121 58498535041007616 36297120474637323921 23010091409714094140625 14524605739135674912669696 9106135496972197033178986641

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -6 30 198 822 3354 15330 76098 386022 1949454 9777630

Decomposition

1.5.ad 4

Base change

This is a primitive isogeny class.