Properties

Label 4.5.am_cu_akq_bcg
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:  $( 1 - 4 x + 5 x^{2} )^{2}( 1 - 2 x + 5 x^{2} )^{2}$
Frobenius angles:  $\pm0.14758361765$, $\pm0.14758361765$, $\pm0.35241638235$, $\pm0.35241638235$
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
$A(\F_{q^r})$ 64 409600 326019136 167772160000 95001825684544 59593168277094400 37730875981310733376 23535616807151861760000 14609158568540870270638144 9094950700166598177187840000

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -6 26 162 682 3114 15626 79122 394842 1960794 9765626

Decomposition

1.5.ae 2 $\times$ 1.5.ac 2

Base change

This is a primitive isogeny class.