Properties

Label 3.11.an_dg_ang
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:  $( 1 - 2 x + 11 x^{2} )( 1 - 11 x + 51 x^{2} - 121 x^{3} + 121 x^{4} )$
Frobenius angles:  $\pm0.0215640055172$, $\pm0.270299311731$, $\pm0.402508885479$
Angle rank:  $3$ (numerical)

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
$A(\F_{q^r})$ 410 1750700 2439798890 3120909864800 4146259914764000 5546939062575392300 7396922271273113068690 9848442391838513252899200 13109235386413189760377623410 17449146419289829121570000000000

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -1 121 1379 14561 159854 1767421 19478409 214330801 2357811209 25937044296

Decomposition

1.11.ac $\times$ 2.11.al_bz

Base change

This is a primitive isogeny class.