Properties

Label 2.17.aj_by
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:  $1 - 9 x + 50 x^{2} - 153 x^{3} + 289 x^{4}$
Frobenius angles:  $\pm0.207100498588$, $\pm0.404445408663$
Angle rank:  $2$ (numerical)
Number field:  4.0.447372.1
Galois group:  $D_4$

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
$A(\F_{q^r})$ 178 89356 24949192 6999791616 2015978331058 582739674698752 168394782386517298 48661501261692100608 14062975351879497100744 4064220154548700275695116

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 9 309 5076 83809 1419849 24142434 410379993 6975801793 118586956500 2015988319029

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.