Properties

Label 3.13.ap_ed_asf
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:  $1 - 15 x + 107 x^{2} - 473 x^{3} + 1391 x^{4} - 2535 x^{5} + 2197 x^{6}$
Frobenius angles:  $\pm0.121512831482$, $\pm0.156505334593$, $\pm0.412789007218$
Angle rank:  $3$ (numerical)
Number field:  6.0.9678431.1
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
$A(\F_{q^r})$ 673 4521887 10714034149 23268151844951 51207217894692733 112616026553178240911 247238464085360202766144 542887462682608448742333191 1192547535212590935925719001921 2619990800980712195952923316943367

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -1 159 2219 28523 371449 4833699 62792680 815860995 10604626025 137858237039

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.