Properties

Label 3.11.an_de_ams
Base Field $\F_{11}$
Dimension $3$
$p$-rank $2$
Does not contain a Jacobian

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Invariants

Base field:  $\F_{11}$
Dimension:  $3$
Weil polynomial:  $1 - 13 x + 82 x^{2} - 330 x^{3} + 902 x^{4} - 1573 x^{5} + 1331 x^{6}$
Frobenius angles:  $\pm0.0593713135806$, $\pm0.214892189705$, $\pm0.437033929118$
Angle rank:  $3$ (numerical)
Number field:  6.0.5910179.1
Galois group:  $S_4\times C_2$

This isogeny class is simple.

Newton polygon

$p$-rank:  $2$
Slopes:  $[0, 0, 1/2, 1/2, 1, 1]$

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
$A(\F_{q^r})$ 400 1692800 2378443600 3110750220800 4167688334560000 5564540830268700800 7402622215673449240400 9848788048888092229683200 13108995802629252949856539600 17449185894269004447078379520000

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -1 117 1343 14513 160684 1773033 19493417 214338321 2357768117 25937102972

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.