Properties

Label 3.11.ao_dr_ape
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:  $1 - 14 x + 95 x^{2} - 394 x^{3} + 1045 x^{4} - 1694 x^{5} + 1331 x^{6}$
Frobenius angles:  $\pm0.0682866536173$, $\pm0.250103379105$, $\pm0.359702241025$
Angle rank:  $3$ (numerical)
Number field:  6.0.34608320.1
Galois group:  The Galois group of this isogeny class is not in the database.

This isogeny class is simple.

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
$A(\F_{q^r})$ 370 1692380 2471954830 3166436210480 4165236927379250 5550232090389737180 7397832084685859743870 9849829411460709265191680 13110200414225233105162398730 17449455696236035073865632889500

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -2 116 1396 14772 160588 1768472 19480802 214360988 2357984782 25937504016

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.