Properties

Label 4.5.al_cg_ahq_ti
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:  $( 1 - 4 x + 5 x^{2} )( 1 - 7 x + 25 x^{2} - 63 x^{3} + 125 x^{4} - 175 x^{5} + 125 x^{6} )$
Frobenius angles:  $\pm0.0923731703714$, $\pm0.14758361765$, $\pm0.243942915084$, $\pm0.536165446792$
Angle rank:  $4$ (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
$A(\F_{q^r})$ 62 323020 227332238 152331063680 102004742170342 61542658281520780 37284327213404217344 23277220076463368394240 14581361287667006692266974 9102397551739387088407677100

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -5 21 115 625 3335 16125 78192 390529 1957075 9773621

Decomposition

1.5.ae $\times$ 3.5.ah_z_acl

Base change

This is a primitive isogeny class.