Properties

Label 2.2.ad_f
Base Field $\F_{2}$
Dimension $2$
$p$-rank $2$
Principally polarizable
Contains a Jacobian

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Invariants

Base field:  $\F_{2}$
Dimension:  $2$
Weil polynomial:  $1 - 3 x + 5 x^{2} - 6 x^{3} + 4 x^{4}$
Frobenius angles:  $\pm0.123548644961$, $\pm0.456881978294$
Angle rank:  $1$ (numerical)
Number field:  \(\Q(\sqrt{-3}, \sqrt{5})\)
Galois group:  $V_4$

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
$A(\F_{q^r})$ 1 19 76 171 961 5776 22051 69939 261364 1113799

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 0 6 9 10 30 87 168 274 513 1086

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.

Additional information

This is the isogeny class of the Jacobian of a function field of class number 1.