Properties

Label 2.19.ao_dh
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:  $1 - 14 x + 85 x^{2} - 266 x^{3} + 361 x^{4}$
Frobenius angles:  $\pm0.0842499841681$, $\pm0.278630291574$
Angle rank:  $2$ (numerical)
Number field:  4.0.14912.2
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
$A(\F_{q^r})$ 167 121409 47234948 17025548297 6131729053647 2212994534939024 798968756034428951 288440385356155507913 104127624997453294352996 37590023951405955004876209

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 6 336 6888 130644 2476366 47039070 893829306 16983502500 322688549064 6131074493536

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.