Properties

Label 2.19.ak_cd
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:  $1 - 10 x + 55 x^{2} - 190 x^{3} + 361 x^{4}$
Frobenius angles:  $\pm0.145032844023$, $\pm0.419866368263$
Angle rank:  $2$ (numerical)
Number field:  4.0.67136.2
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
$A(\F_{q^r})$ 217 133889 47604592 16956907961 6128712789577 2213946379307264 799112552306949937 288447189159454075625 104127279229248736876912 37589953538027409138268929

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 10 372 6940 130116 2475150 47059302 893990170 16983903108 322687477540 6131063008852

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.