Properties

Label 2.2.ab_ab
Base Field $\F_{2}$
Dimension $2$
$p$-rank $2$
Not principally polarizable
Does not contain a Jacobian

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Invariants

Base field:  $\F_{2}$
Dimension:  $2$
Weil polynomial:  $1 - x - x^{2} - 2 x^{3} + 4 x^{4}$
Frobenius angles:  $\pm0.0516399385854$, $\pm0.718306605252$
Angle rank:  $1$ (numerical)
Number field:  \(\Q(\sqrt{-3}, \sqrt{-7})\)
Galois group:  $C_2^2$

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 is not principally polarizable, and therefore does not contain a Jacobian.

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 1 7 16 259 751 3136 18103 58275 258064 1109227

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 2 2 -1 18 22 47 142 226 503 1082

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.