Properties

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

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Invariants

Base field:  $\F_{2^2}$
Dimension:  $2$
Weil polynomial:  $1+5x^{2}+16x^{4}$
Frobenius angles:  $\pm0.357450520704$, $\pm0.642549479296$
Angle rank:  $1$ (numerical)
Number field:  \(\Q(\sqrt{3}, \sqrt{-13})\)
Galois group:  $V_4$

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
$A(\F_{q^r})$ 22 484 3982 69696 1048102 15856324 268468222 4356000000 68719368982 1098517802404

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 5 27 65 271 1025 3867 16385 66463 262145 1047627

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.