Properties

Label 2.4.a_b
Base Field $\F_{2^2}$
Dimension $2$
Ordinary No
$p$-rank $2$
Principally polarizable Yes
Contains a Jacobian Yes

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Invariants

Base field:  $\F_{2^2}$
Dimension:  $2$
Weil polynomial:  $1 + x^{2} + 16 x^{4}$
Frobenius angles:  $\pm0.269946543837$, $\pm0.730053456163$
Angle rank:  $1$ (numerical)
Number field:  \(\Q(i, \sqrt{7})\)
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 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
$A(\F_{q^r})$ 18 324 4050 82944 1049778 16402500 268410258 4236447744 68719950450 1102033849284

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 5 19 65 319 1025 4003 16385 64639 262145 1050979

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.