Properties

Label 4.5.al_cc_agj_pe
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:  $( 1 - 4 x + 5 x^{2} )^{2}( 1 - 3 x + 4 x^{2} - 15 x^{3} + 25 x^{4} )$
Frobenius angles:  $\pm0.0673911931187$, $\pm0.14758361765$, $\pm0.14758361765$, $\pm0.599275473548$
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 230400 173606976 148163788800 101953185785328 60838550898278400 37541881767426974832 23478119514722480947200 14587053626073722920017984 9093036552015063765432960000

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -5 13 82 605 3335 15946 78731 393885 1957834 9763573

Decomposition

1.5.ae 2 $\times$ 2.5.ad_e

Base change

This is a primitive isogeny class.