Properties

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

Learn more about

Invariants

Base field:  $\F_{19}$
Dimension:  $2$
Weil polynomial:  $1 - 12 x + 69 x^{2} - 228 x^{3} + 361 x^{4}$
Frobenius angles:  $\pm0.106312411237$, $\pm0.357895350441$
Angle rank:  $2$ (numerical)
Number field:  4.0.12625.1
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
$A(\F_{q^r})$ 191 128161 47539136 16981973305 6125692347071 2213008391520256 799044670009668791 288449384824034140905 104127995238661094476736 37589995770672827115745441

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 8 356 6932 130308 2473928 47039366 893914232 16984032388 322689696428 6131069897156

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.