Properties

Label 1.13.a
Base Field $\F_{13}$
Dimension $1$
$p$-rank $0$
Principally polarizable
Contains a Jacobian

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Invariants

Base field:  $\F_{13}$
Dimension:  $1$
Weil polynomial:  $1 + 13 x^{2}$
Frobenius angles:  $\pm0.5$
Angle rank:  $0$ (numerical)
Number field:  \(\Q(\sqrt{-13}) \)
Galois group:  $C_2$

This isogeny class is simple.

Newton polygon

This isogeny class is supersingular.

$p$-rank:  $0$
Slopes:  $[1/2, 1/2]$

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
$A(\F_{q^r})$ 14 196 2198 28224 371294 4831204 62748518 815673600 10604499374 137859234436

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 14 196 2198 28224 371294 4831204 62748518 815673600 10604499374 137859234436

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.