Properties

Label 3.11.ar_ey_avc
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:  $( 1 - 6 x + 11 x^{2} )( 1 - 11 x + 51 x^{2} - 121 x^{3} + 121 x^{4} )$
Frobenius angles:  $\pm0.0215640055172$, $\pm0.140218899004$, $\pm0.270299311731$
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
$A(\F_{q^r})$ 246 1350540 2306399814 3148346435040 4179274751901216 5556461382098239500 7397451961997088144126 9848654078179185243296640 13109805387201623446083283614 17449427983357018525876560000000

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -5 89 1303 14689 161130 1770461 19479805 214335409 2357913733 25937462824

Decomposition

1.11.ag $\times$ 2.11.al_bz

Base change

This is a primitive isogeny class.