Properties

Label 4.5.am_cr_ajt_zk
Base Field $\F_{5}$
Dimension $4$
$p$-rank $3$
Does not contain a Jacobian

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Invariants

Base field:  $\F_{5}$
Dimension:  $4$
Weil polynomial:  $( 1 - 4 x + 5 x^{2} )( 1 - 8 x + 32 x^{2} - 85 x^{3} + 160 x^{4} - 200 x^{5} + 125 x^{6} )$
Frobenius angles:  $\pm0.0657033817182$, $\pm0.14758361765$, $\pm0.238557099512$, $\pm0.475140873389$
Angle rank:  $4$ (numerical)

Newton polygon

$p$-rank:  $3$
Slopes:  $[0, 0, 0, 1/2, 1/2, 1, 1, 1]$

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
$A(\F_{q^r})$ 50 305500 241563050 148057520000 97494032110250 61265218325369500 37488695779133845450 23220052872659847360000 14536417880726821090275200 9100235005249189095028637500

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -6 20 123 608 3194 16055 78618 389568 1951044 9771300

Decomposition

1.5.ae $\times$ 3.5.ai_bg_adh

Base change

This is a primitive isogeny class.