Properties

Label 4.5.al_cj_ain_we
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:  $( 1 - 4 x + 5 x^{2} )^{2}( 1 - 3 x + 11 x^{2} - 15 x^{3} + 25 x^{4} )$
Frobenius angles:  $\pm0.14758361765$, $\pm0.14758361765$, $\pm0.300933478836$, $\pm0.472779926746$
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
$A(\F_{q^r})$ 76 418000 288734716 157943808000 98651495818816 61458772341538000 37682909808445408156 23329649713854578688000 14571525193312758813944236 9105474366436704604480000000

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -5 27 145 647 3230 16107 79025 391407 1955755 9776922

Decomposition

1.5.ae 2 $\times$ 2.5.ad_l

Base change

This is a primitive isogeny class.