Properties

Label 2.19.al_cn
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:  $1 - 11 x + 65 x^{2} - 209 x^{3} + 361 x^{4}$
Frobenius angles:  $\pm0.18390806493$, $\pm0.36059024889$
Angle rank:  $2$ (numerical)
Number field:  4.0.26533.1
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
$A(\F_{q^r})$ 207 133929 48346713 17064295677 6132261832272 2213364397163049 799043845092737661 288445952175817883733 104127441596475871887171 37589936977009790399856384

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 9 371 7047 130939 2476584 47046935 893913309 16983830275 322687980711 6131060307686

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.