Properties

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

Learn more about

Invariants

Base field:  $\F_{11}$
Dimension:  $3$
Weil polynomial:  $1 - 13 x + 81 x^{2} - 324 x^{3} + 891 x^{4} - 1573 x^{5} + 1331 x^{6}$
Frobenius angles:  $\pm0.0329532391161$, $\pm0.203794694889$, $\pm0.447810262494$
Angle rank:  $3$ (numerical)
Number field:  6.0.251429824.2
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
$A(\F_{q^r})$ 394 1660316 2341108600 3093241761904 4164698578969294 5564142906912161600 7401563657852631349154 9847942574399766457621504 13108666354797185943780898600 17449061641059486538116003479996

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -1 115 1322 14431 160569 1772908 19490631 214319919 2357708858 25936918275

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.