Properties

Label 3.11.ap_ec_are
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:  $( 1 - 4 x + 11 x^{2} )( 1 - 11 x + 51 x^{2} - 121 x^{3} + 121 x^{4} )$
Frobenius angles:  $\pm0.0215640055172$, $\pm0.270299311731$, $\pm0.2939628337$
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
$A(\F_{q^r})$ 328 1600640 2457351400 3182642147840 4168977020568448 5542992311720528000 7390812615085830357608 9846801822698305327319040 13109676769529277216077482600 17449575247994767399554560000000

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -3 109 1389 14849 160732 1766161 19462307 214295089 2357890599 25937681724

Decomposition

1.11.ae $\times$ 2.11.al_bz

Base change

This is a primitive isogeny class.