Properties

Label 3.13.aq_es_avj
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:  $1 - 16 x + 122 x^{2} - 555 x^{3} + 1586 x^{4} - 2704 x^{5} + 2197 x^{6}$
Frobenius angles:  $\pm0.107742898637$, $\pm0.227592439174$, $\pm0.325764106975$
Angle rank:  $3$ (numerical)
Number field:  6.0.11666459.1
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
$A(\F_{q^r})$ 631 4531211 11072490799 23666737082339 51292846885738891 112441506056786691707 247051516374572851920007 542815558600951600440704579 1192556086446545013697266713152 2620009943543046531274372722139691

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -2 158 2293 29010 372068 4826213 62745212 815752946 10604702068 137859244278

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.