Properties

Label 2.19.al_cm
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:  $1-11x+64x^{2}-209x^{3}+361x^{4}$
Frobenius angles:  $\pm0.16580892597$, $\pm0.37094658213$
Angle rank:  $2$ (numerical)
Number field:  4.0.349112.1
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
$A(\F_{q^r})$ 206 133076 48115832 17034792608 6130763962866 2213470309936064 799069449922614818 288448112752124296832 104127537296738062291928 37589940421461346132563156

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 9 369 7014 130713 2475979 47049186 893941953 16983957489 322688277282 6131060869489

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.