Properties

Label 4.5.an_df_ams_bie
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:  $( 1 - 4 x + 5 x^{2} )( 1 - 3 x + 5 x^{2} )^{3}$
Frobenius angles:  $\pm0.14758361765$, $\pm0.265942140215$, $\pm0.265942140215$, $\pm0.265942140215$
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
$A(\F_{q^r})$ 54 393660 364290048 196830000000 103259791417374 59657070843002880 36794213184728145438 23140362291178680000000 14542119714034827758444544 9103779873771429029456166300

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -7 23 176 787 3373 15638 77161 388227 1951808 9775103

Decomposition

1.5.ae $\times$ 1.5.ad 3

Base change

This is a primitive isogeny class.