Properties

Label 3.11.ao_dp_aor
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:  $1 - 14 x + 93 x^{2} - 381 x^{3} + 1023 x^{4} - 1694 x^{5} + 1331 x^{6}$
Frobenius angles:  $\pm0.0701462554279$, $\pm0.192008360592$, $\pm0.39925392621$
Angle rank:  $3$ (numerical)
Number field:  6.0.62037703.1
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
$A(\F_{q^r})$ 359 1628783 2392406156 3128776499407 4167652624327664 5562592194686635472 7404414418494749999401 9850940839839779776909423 13109700078781101300038026556 17449103909118474912829997796608

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -2 112 1351 14596 160683 1772413 19498134 214385172 2357894791 25936981107

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.