Properties

Label 2.19.ap_dp
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:  $1 - 15 x + 93 x^{2} - 285 x^{3} + 361 x^{4}$
Frobenius angles:  $\pm0.0482018232348$, $\pm0.238558256044$
Angle rank:  $2$ (numerical)
Number field:  4.0.1525.1
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
$A(\F_{q^r})$ 155 117025 46735445 16999168525 6131808122000 2213056283091025 798953364541302545 288435612056346033525 104126946427712916323255 37589961062970636364000000

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 5 323 6815 130443 2476400 47040383 893812085 16983221443 322686446195 6131064236198

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.