Properties

Label 2.4.ac_a
Base Field $\F_{2^2}$
Dimension $2$
$p$-rank $0$
Principally polarizable
Does not contain a Jacobian

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Invariants

Base field:  $\F_{2^2}$
Dimension:  $2$
Weil polynomial:  $( 1 - 2 x )^{2}( 1 + 2 x + 4 x^{2} )$
Frobenius angles:  $0.0$, $0.0$, $\pm0.666666666667$
Angle rank:  $0$ (numerical)

Newton polygon

This isogeny class is supersingular.

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

Point counts

This isogeny class is principally polarizable, but does not contain a Jacobian.

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 7 189 2401 61425 1015777 15752961 266338177 4278189825 68184176641 1098437884929

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 3 13 33 241 993 3841 16257 65281 260097 1047553

Decomposition

1.4.ae $\times$ 1.4.c

Base change

This is a primitive isogeny class.