Properties

Label 2.17.am_cr
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:  $( 1 - 7 x + 17 x^{2} )( 1 - 5 x + 17 x^{2} )$
Frobenius angles:  $\pm0.177280642489$, $\pm0.292637436158$
Angle rank:  $2$ (numerical)

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
$A(\F_{q^r})$ 143 82225 24856832 7047093625 2019558358103 582683913011200 168373478252203367 48660930058145315625 14063093622411016671488 4064232651550128628338625

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 6 284 5058 84372 1422366 24140126 410328078 6975719908 118587953826 2015994517964

Decomposition

1.17.ah $\times$ 1.17.af

Base change

This is a primitive isogeny class.