Properties

Label 3.11.aq_en_atd
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:  $( 1 - 5 x + 11 x^{2} )( 1 - 11 x + 51 x^{2} - 121 x^{3} + 121 x^{4} )$
Frobenius angles:  $\pm0.0215640055172$, $\pm0.22822922288$, $\pm0.270299311731$
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
$A(\F_{q^r})$ 287 1488095 2408204372 3188429549375 4185769049802032 5552464513772202320 7393096432039702835437 9846257309200912727019375 13108906041999147831913733012 17449225520380929509044580000000

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -4 100 1361 14876 161381 1769185 19468326 214283236 2357751971 25937161875

Decomposition

1.11.af $\times$ 2.11.al_bz

Base change

This is a primitive isogeny class.