Properties

Label 4.5.am_cu_akq_bcf
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:  $( 1 - 3 x + 5 x^{2} )^{2}( 1 - 6 x + 17 x^{2} - 30 x^{3} + 25 x^{4} )$
Frobenius angles:  $\pm0.0512862249088$, $\pm0.265942140215$, $\pm0.265942140215$, $\pm0.384619558242$
Angle rank:  $2$ (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
$A(\F_{q^r})$ 63 403137 321076224 165538130625 93198017193183 57988092160180224 36809102946159389727 23197544263794809120625 14538268526711324681567232 9095618997158239136593946097

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -6 26 162 678 3054 15194 77190 389190 1951290 9766346

Decomposition

1.5.ad 2 $\times$ 2.5.ag_r

Base change

This is a primitive isogeny class.