Properties

Label 4.5.ao_dp_aoo_bnk
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:  $( 1 - 4 x + 5 x^{2} )^{2}( 1 - 3 x + 5 x^{2} )^{2}$
Frobenius angles:  $\pm0.14758361765$, $\pm0.14758361765$, $\pm0.265942140215$, $\pm0.265942140215$
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
$A(\F_{q^r})$ 36 291600 308634624 186624000000 103876170945156 60838550898278400 37298113629404912964 23271370696986624000000 14559654807532466321826816 9101424859935705708138090000

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -8 16 154 752 3392 15946 78224 390432 1954162 9772576

Decomposition

1.5.ae 2 $\times$ 1.5.ad 2

Base change

This is a primitive isogeny class.