Properties

Label 3.11.ao_do_aol
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:  $1 - 14 x + 92 x^{2} - 375 x^{3} + 1012 x^{4} - 1694 x^{5} + 1331 x^{6}$
Frobenius angles:  $\pm0.0370510590969$, $\pm0.180631153359$, $\pm0.411625911318$
Angle rank:  $3$ (numerical)
Number field:  6.0.31633587.1
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
$A(\F_{q^r})$ 353 1595207 2349243593 3102660067723 4159230790999603 5560792831378351367 7403333932962076457113 9849975362083673459044947 13109193017918985425051840192 17448936333570654521812839442367

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -2 110 1327 14474 160358 1771841 19495292 214364162 2357803588 25936732010

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.