Properties

Label 2.4.a_a
Base Field $\F_{2^2}$
Dimension $2$
$p$-rank $0$
Principally polarizable
Contains a Jacobian

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Invariants

Base field:  $\F_{2^2}$
Dimension:  $2$
Weil polynomial:  $1 + 16 x^{4}$
Frobenius angles:  $\pm0.25$, $\pm0.75$
Angle rank:  $0$ (numerical)
Number field:  \(\Q(\zeta_{8})\)
Galois group:  $C_2^2$

This isogeny class is simple.

Newton polygon

This isogeny class is supersingular.

$p$-rank:  $0$
Slopes:  $[1/2, 1/2, 1/2, 1/2]$

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
$A(\F_{q^r})$ 17 289 4097 83521 1048577 16785409 268435457 4228250625 68719476737 1099513724929

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 5 17 65 321 1025 4097 16385 64513 262145 1048577

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.