Properties

Label 3.11.ap_ec_arc
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:  $( 1 - 6 x + 11 x^{2} )( 1 - 9 x + 41 x^{2} - 99 x^{3} + 121 x^{4} )$
Frobenius angles:  $\pm0.140218899004$, $\pm0.178435994483$, $\pm0.329700688269$
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
$A(\F_{q^r})$ 330 1609740 2473874370 3209654147040 4199877907500000 5567066737264939500 7404072869192276970330 9851848788229557789651840 13110722132111459976464687970 17449427983357018525876560000000

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -3 109 1395 14969 161922 1773841 19497237 214404929 2358078615 25937462824

Decomposition

1.11.ag $\times$ 2.11.aj_bp

Base change

This is a primitive isogeny class.