Properties

Label 3.11.ao_dq_aox
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:  $1 - 14 x + 94 x^{2} - 387 x^{3} + 1034 x^{4} - 1694 x^{5} + 1331 x^{6}$
Frobenius angles:  $\pm0.0887296077117$, $\pm0.207434636458$, $\pm0.384783505598$
Angle rank:  $3$ (numerical)
Number field:  6.0.59264075.1
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
$A(\F_{q^r})$ 365 1662575 2435836625 3154139198075 4174009280277875 5562052815248264375 7403914687828017042685 9851215672838615019917075 13109998683927496431864536000 17449202308396969907023369109375

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -2 114 1375 14714 160928 1772241 19496818 214391154 2357948500 25937127374

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.