Properties

Label 3.11.an_df_amz
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:  $1 - 13 x + 83 x^{2} - 337 x^{3} + 913 x^{4} - 1573 x^{5} + 1331 x^{6}$
Frobenius angles:  $\pm0.0419333658373$, $\pm0.241588088023$, $\pm0.421886769942$
Angle rank:  $3$ (numerical)
Number field:  6.0.403627375.1
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
$A(\F_{q^r})$ 405 1721655 2409010875 3116197271655 4157729688909375 5556186788680110375 7399646802705714626880 9848266864767932173362855 13108896537245525348720479125 17449123886179266530194197159375

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -1 119 1361 14539 160299 1770371 19485584 214326979 2357750261 25937010799

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.