Properties

Label 4.5.am_cr_ajs_zg
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:  $( 1 - 4 x + 5 x^{2} )^{2}( 1 - 4 x + 11 x^{2} - 20 x^{3} + 25 x^{4} )$
Frobenius angles:  $\pm0.14758361765$, $\pm0.14758361765$, $\pm0.185749715683$, $\pm0.480916950984$
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
$A(\F_{q^r})$ 52 317200 251539600 156234956800 102588049661812 63272170368160000 38056342149202802932 23345947240459252531200 14551929298156324491648400 9095389395817645702197130000

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -6 20 126 640 3354 16562 79794 391680 1953126 9766100

Decomposition

1.5.ae 2 $\times$ 2.5.ae_l

Base change

This is a primitive isogeny class.