Properties

Label 3.11.an_dd_aml
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:  $1 - 13 x + 81 x^{2} - 323 x^{3} + 891 x^{4} - 1573 x^{5} + 1331 x^{6}$
Frobenius angles:  $\pm0.0791621428929$, $\pm0.186215857244$, $\pm0.449854739171$
Angle rank:  $3$ (numerical)
Number field:  6.0.343424015.1
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
$A(\F_{q^r})$ 395 1664135 2348089745 3104558667815 4176130023943625 5571961697896671935 7405752543653767390720 9849912225117183937385415 13109511281148410851245991955 17449376484479368605970901603375

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -1 115 1325 14483 161009 1775395 19501656 214362787 2357860835 25937386275

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.