Properties

Label 3.11.an_dc_ame
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:  $( 1 - 6 x + 11 x^{2} )( 1 - 7 x + 27 x^{2} - 77 x^{3} + 121 x^{4} )$
Frobenius angles:  $\pm0.116678659763$, $\pm0.140218899004$, $\pm0.461158112795$
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
$A(\F_{q^r})$ 390 1635660 2317941990 3097612908000 4183049482716000 5578410303754879500 7408941997991615729310 9851543525232829029168000 13110413880450992321633581710 17449729852153104431626656384000

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -1 113 1307 14449 161274 1777445 19510049 214398289 2358023177 25937911528

Decomposition

1.11.ag $\times$ 2.11.ah_bb

Base change

This is a primitive isogeny class.