Properties

Label 4.5.am_cq_ajk_yg
Base Field $\F_{5}$
Dimension $4$
$p$-rank $3$
Does not contain a Jacobian

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Invariants

Base field:  $\F_{5}$
Dimension:  $4$
Weil polynomial:  $( 1 + 5 x^{2} )( 1 - 4 x + 5 x^{2} )^{3}$
Frobenius angles:  $\pm0.14758361765$, $\pm0.14758361765$, $\pm0.14758361765$, $\pm0.5$
Angle rank:  $1$ (numerical)

Newton polygon

$p$-rank:  $3$
Slopes:  $[0, 0, 0, 1/2, 1/2, 1, 1, 1]$

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
$A(\F_{q^r})$ 48 288000 228796848 150994944000 102624949503408 63336001057056000 38055879314533355568 23397172002403909632000 14584065785848469246657328 9102096763908314775156000000

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -6 18 114 618 3354 16578 79794 392538 1957434 9773298

Decomposition

1.5.ae 3 $\times$ 1.5.a

Base change

This is a primitive isogeny class.