Properties

Label 3.11.ap_eb_aqx
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:  $1 - 15 x + 105 x^{2} - 439 x^{3} + 1155 x^{4} - 1815 x^{5} + 1331 x^{6}$
Frobenius angles:  $\pm0.0556623249738$, $\pm0.201555355312$, $\pm0.34409147013$
Angle rank:  $3$ (numerical)
Number field:  6.0.4612383.1
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
$A(\F_{q^r})$ 323 1570103 2415897557 3161058537943 4171399934792653 5554184265401716727 7399088933596202473408 9849996737971517154033063 13110060625941766333124234375 17449264171265659608094307485703

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -3 107 1365 14747 160827 1769735 19484112 214364627 2357959641 25937219327

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.