Properties

Label 2.17.ap_dm
Base Field $\F_{17}$
Dimension $2$
$p$-rank $2$
Principally polarizable
Does not contain a Jacobian

Learn more about

Invariants

Base field:  $\F_{17}$
Dimension:  $2$
Weil polynomial:  $( 1 - 8 x + 17 x^{2} )( 1 - 7 x + 17 x^{2} )$
Frobenius angles:  $\pm0.0779791303774$, $\pm0.177280642489$
Angle rank:  $2$ (numerical)

Newton polygon

This isogeny class is ordinary.

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

Point counts

This isogeny class is principally polarizable, but does not contain a Jacobian.

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 110 71500 23703680 6978400000 2018018233550 582830824576000 168392298144692270 48661929864662400000 14063108690397910183040 4064231487841064613287500

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 3 245 4824 83553 1421283 24146210 410373939 6975863233 118588080888 2015993940725

Decomposition

1.17.ai $\times$ 1.17.ah

Base change

This is a primitive isogeny class.