Properties

Label 3.11.aq_em_asw
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:  $( 1 - 6 x + 11 x^{2} )( 1 - 10 x + 45 x^{2} - 110 x^{3} + 121 x^{4} )$
Frobenius angles:  $\pm0.0820279942768$, $\pm0.140218899004$, $\pm0.318205720493$
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
$A(\F_{q^r})$ 282 1456812 2361378888 3155955935328 4177922312632602 5559031135945425600 7401838896556089732462 9851807652998016288240000 13111220218893013578817121688 17449833087139019509072187916012

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -4 98 1334 14722 161076 1771280 19491356 214404034 2358168194 25938064978

Decomposition

1.11.ag $\times$ 2.11.ak_bt

Base change

This is a primitive isogeny class.