Properties

Label 4.5.al_ch_ahx_ue
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:  $( 1 - 4 x + 5 x^{2} )^{2}( 1 - 3 x + 9 x^{2} - 15 x^{3} + 25 x^{4} )$
Frobenius angles:  $\pm0.14758361765$, $\pm0.14758361765$, $\pm0.235523574971$, $\pm0.521566933142$
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
$A(\F_{q^r})$ 68 360400 252268916 159798476800 104455895241728 62590163252952400 37542139214220476372 23275134774468653875200 14565881008837190764198724 9097810705223061110824960000

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -5 23 127 655 3410 16391 78731 390495 1954999 9768698

Decomposition

1.5.ae 2 $\times$ 2.5.ad_j

Base change

This is a primitive isogeny class.