Properties

Label 3.13.ap_eg_atc
Base Field $\F_{13}$
Dimension $3$
$p$-rank $3$
Does not contain a Jacobian

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Invariants

Base field:  $\F_{13}$
Dimension:  $3$
Weil polynomial:  $1 - 15 x + 110 x^{2} - 496 x^{3} + 1430 x^{4} - 2535 x^{5} + 2197 x^{6}$
Frobenius angles:  $\pm0.0520504550069$, $\pm0.271344466885$, $\pm0.356632440861$
Angle rank:  $3$ (numerical)
Number field:  6.0.5611187.1
Galois group:  The Galois group of this isogeny class is not in the database.

This isogeny class is simple.

Newton polygon

This isogeny class is ordinary.

$p$-rank:  $3$
Slopes:  $[0, 0, 0, 1, 1, 1]$

Point counts

This isogeny class does not contain a Jacobian, and it is unknown whether it is principally polarizable.

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 692 4694528 11023593908 23408287410176 51013925488225472 112265907265155318272 246978771567299420628692 542792262946231369189203968 1192545125878570895730884198324 2620002402814583034388045374291968

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -1 165 2285 28697 370044 4818669 62726733 815717937 10604604599 137858847500

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.