# Properties

 Label 3.11.ar_ey_avc Base Field $\F_{11}$ Dimension $3$ $p$-rank $3$ Does not contain a Jacobian

## 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.

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 246 1350540 2306399814 3148346435040 4179274751901216 5556461382098239500 7397451961997088144126 9848654078179185243296640 13109805387201623446083283614 17449427983357018525876560000000

 $r$ 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.