Properties

Label 3.11.an_de_amr
Base Field $\F_{11}$
Dimension $3$
$p$-rank $3$
Does not contain a Jacobian

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Invariants

Base field:  $\F_{11}$
Dimension:  $3$
Weil polynomial:  $1 - 13 x + 82 x^{2} - 329 x^{3} + 902 x^{4} - 1573 x^{5} + 1331 x^{6}$
Frobenius angles:  $\pm0.0935398046292$, $\pm0.197577243604$, $\pm0.439402580349$
Angle rank:  $3$ (numerical)
Number field:  6.0.380456496.1
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
$A(\F_{q^r})$ 401 1696631 2385435116 3122053838019 4178977468600411 5571979389613552496 7406281847411912937481 9850277695137678031977099 13109520296723840105533567364 17449327630043840574870306343391

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -1 117 1346 14565 161119 1775400 19503049 214370741 2357862458 25937313657

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.