Properties

Label 2.3.a_b
Base Field $\F_{3}$
Dimension $2$
$p$-rank $2$
Principally polarizable
Contains a Jacobian

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Invariants

Base field:  $\F_{3}$
Dimension:  $2$
Weil polynomial:  $1 + x^{2} + 9 x^{4}$
Frobenius angles:  $\pm0.276650189519$, $\pm0.723349810481$
Angle rank:  $1$ (numerical)
Number field:  \(\Q(\sqrt{5}, \sqrt{-7})\)
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
$A(\F_{q^r})$ 11 121 704 9801 59411 495616 4778939 41409225 387459776 3529666921

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 4 12 28 116 244 678 2188 6308 19684 59772

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.