Properties

Label 2.19.ak_ca
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:  $1 - 10 x + 52 x^{2} - 190 x^{3} + 361 x^{4}$
Frobenius angles:  $\pm0.0969409553786$, $\pm0.438146995596$
Angle rank:  $2$ (numerical)
Number field:  4.0.38720.3
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
$A(\F_{q^r})$ 214 131396 46981774 16884386000 6124262327854 2213732987579876 799087397110427254 288444712420098176000 104127327060645758306374 37589992633096691075945316

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 10 366 6850 129558 2473350 47054766 893962030 16983757278 322687625770 6131069385406

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.