Properties

Label 2.13.ai_bg
Base Field $\F_{13}$
Dimension $2$
$p$-rank $2$
Principally polarizable
Contains a Jacobian

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Invariants

Base field:  $\F_{13}$
Dimension:  $2$
Weil polynomial:  $1 - 8 x + 32 x^{2} - 104 x^{3} + 169 x^{4}$
Frobenius angles:  $\pm0.0370621216586$, $\pm0.462937878341$
Angle rank:  $1$ (numerical)
Number field:  \(\Q(i, \sqrt{10})\)
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
$A(\F_{q^r})$ 90 28260 4705290 798627600 137233172250 23298083455140 3937418050935690 665361008507289600 112452424073098948890 19004963775070323766500

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 6 170 2142 27958 369606 4826810 62749182 815662558 10604218086 137858491850

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.