Properties

Label 4.5.am_cs_akb_bak
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:  $( 1 - 4 x + 5 x^{2} )( 1 - 3 x + 5 x^{2} )( 1 - 5 x + 13 x^{2} - 25 x^{3} + 25 x^{4} )$
Frobenius angles:  $\pm0.0878807261908$, $\pm0.14758361765$, $\pm0.265942140215$, $\pm0.450170915301$
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
$A(\F_{q^r})$ 54 335340 265153824 152646768000 96425619575904 60878289193562880 37608663565748948454 23298326743389451200000 14551714461451081885255584 9103624378553472574290739200

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -6 22 135 626 3159 15955 78870 390882 1953099 9774937

Decomposition

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

Base change

This is a primitive isogeny class.