Properties

Label 2.17.am_cn
Base Field $\F_{17}$
Dimension $2$
$p$-rank $2$
Principally polarizable
Contains a Jacobian

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Invariants

Base field:  $\F_{17}$
Dimension:  $2$
Weil polynomial:  $1 - 12 x + 65 x^{2} - 204 x^{3} + 289 x^{4}$
Frobenius angles:  $\pm0.0157896134134$, $\pm0.349122946747$
Angle rank:  $1$ (numerical)
Number field:  \(\Q(\sqrt{-3}, \sqrt{5})\)
Galois group:  $V_4$

This isogeny class is simple.

Newton polygon

This isogeny class is ordinary.

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

Point counts

This isogeny class contains a Jacobian, and hence is principally polarizable.

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 139 79369 24128176 6943914441 2010360903259 582168877086976 168359278701453979 48661044555091420809 14063084451918975425584 4064226529530741241632649

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 6 276 4914 83140 1415886 24118782 410293470 6975736324 118587876498 2015991481236

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.