Properties

Label 2.2.ab_d
Base Field $\F_{2}$
Dimension $2$
Ordinary No
$p$-rank $2$
Principally polarizable Yes
Contains a Jacobian Yes

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Invariants

Base field:  $\F_{2}$
Dimension:  $2$
Weil polynomial:  $1 - x + 3 x^{2} - 2 x^{3} + 4 x^{4}$
Frobenius angles:  $\pm0.306143893905$, $\pm0.570118980449$
Angle rank:  $2$ (numerical)
Number field:  4.0.1025.1
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
$A(\F_{q^r})$ 5 55 80 275 1375 3520 11555 66275 302480 1073875

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 2 10 11 18 42 55 86 258 587 1050

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.