Properties

Label 4.5.an_dd_amd_bgi
Base Field $\F_{5}$
Dimension $4$
$p$-rank $2$
Does not contain a Jacobian

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Invariants

Base field:  $\F_{5}$
Dimension:  $4$
Weil polynomial:  $( 1 - 4 x + 5 x^{2} )^{2}( 1 - 5 x + 15 x^{2} - 25 x^{3} + 25 x^{4} )$
Frobenius angles:  $\pm0.14758361765$, $\pm0.14758361765$, $\pm0.2$, $\pm0.4$
Angle rank:  $1$ (numerical)

Newton polygon

$p$-rank:  $2$
Slopes:  $[0, 0, 1/2, 1/2, 1/2, 1/2, 1, 1]$

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
$A(\F_{q^r})$ 44 312400 285043484 166666649600 100060969290304 61906285437739600 38089735991599372124 23446514423076677222400 14550041109224787799036844 9084194718280899304552960000

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -7 19 143 679 3278 16219 79863 393359 1952873 9754074

Decomposition

1.5.ae 2 $\times$ 2.5.af_p

Base change

This is a primitive isogeny class.