Properties

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

Learn more about

Invariants

Base field:  $\F_{5}$
Dimension:  $4$
Weil polynomial:  $( 1 - 4 x + 5 x^{2} )( 1 - 3 x + 5 x^{2} )( 1 - 6 x + 17 x^{2} - 30 x^{3} + 25 x^{4} )$
Frobenius angles:  $\pm0.0512862249088$, $\pm0.14758361765$, $\pm0.265942140215$, $\pm0.384619558242$
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
$A(\F_{q^r})$ 42 298620 272022912 156954672000 93754335863202 59136518882488320 37313207307614283906 23328876403474294464000 14555798976392853728830848 9093266094421158595971587100

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -7 19 140 643 3073 15502 78253 391395 1953644 9763819

Decomposition

1.5.ae $\times$ 1.5.ad $\times$ 2.5.ag_r

Base change

This is a primitive isogeny class.