Properties

Label 2.19.ao_dj
Base Field $\F_{19}$
Dimension $2$
$p$-rank $2$
Principally polarizable
Contains a Jacobian

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Invariants

Base field:  $\F_{19}$
Dimension:  $2$
Weil polynomial:  $( 1 - 7 x + 19 x^{2} )^{2}$
Frobenius angles:  $\pm0.203259864187$, $\pm0.203259864187$
Angle rank:  $1$ (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
$A(\F_{q^r})$ 169 123201 47831056 17140831929 6146645853049 2214310804183296 799032354409893409 288437997911468525289 104126719963943210135056 37589913051239921148065601

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 6 340 6972 131524 2482386 47067046 893900454 16983361924 322685744388 6131056405300

Decomposition

1.19.ah 2

Base change

This is a primitive isogeny class.