Properties

Label 2.4.ac_e
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:  $1 - 2 x + 4 x^{2} - 8 x^{3} + 16 x^{4}$
Frobenius angles:  $\pm0.2$, $\pm0.6$
Angle rank:  $0$ (numerical)
Number field:  \(\Q(\zeta_{5})\)
Galois group:  $C_4$

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
$A(\F_{q^r})$ 11 341 3641 69905 1185921 17043521 266354561 4311810305 68585520641 1095222947841

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 3 21 57 273 1153 4161 16257 65793 261633 1044481

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.