Properties

Label 3.11.an_dc_amf
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:  $1 - 13 x + 80 x^{2} - 317 x^{3} + 880 x^{4} - 1573 x^{5} + 1331 x^{6}$
Frobenius angles:  $\pm0.0574705996813$, $\pm0.177271568763$, $\pm0.459404600808$
Angle rank:  $3$ (numerical)
Number field:  6.0.16537520.2
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
$A(\F_{q^r})$ 389 1631855 2310964976 3086263719155 4171462217405179 5570225925550488320 7404286854219691858769 9849201386810600120640395 13109371568696073102909347216 17449351996087422238032233201375

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -1 113 1304 14397 160829 1774844 19497799 214347317 2357835704 25937349873

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.