Properties

Label 2.81.abd_oe
Base Field $\F_{3^{4}}$
Dimension $2$
Ordinary Yes
$p$-rank $2$
Principally polarizable Yes
Contains a Jacobian Yes

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Invariants

Base field:  $\F_{3^{4}}$
Dimension:  $2$
L-polynomial:  $1 - 29 x + 368 x^{2} - 2349 x^{3} + 6561 x^{4}$
Frobenius angles:  $\pm0.128118350588$, $\pm0.257159505691$
Angle rank:  $2$ (numerical)
Number field:  4.0.608056.1
Galois group:  $D_{4}$
Jacobians:  24

This isogeny class is simple and geometrically simple.

Newton polygon

This isogeny class is ordinary.

$p$-rank:  $2$
Slopes:  $[0, 0, 1, 1]$

Point counts

This isogeny class contains the Jacobians of 24 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 4552 42370016 282738266752 1853604985288576 12158098148309661512 79766627057572417624064 523347663379783912639315208 3433683822378503778807242817024 22528399584026209958825841702654592 147808829487054014599978118831406654176

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 53 6457 532022 43060305 3486908493 282430187902 22876793781741 1853020189977569 150094635557415062 12157665465037360777

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{3^{4}}$
The endomorphism algebra of this simple isogeny class is 4.0.608056.1.
All geometric endomorphisms are defined over $\F_{3^{4}}$.

Base change

This is a primitive isogeny class.

Twists

Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.81.bd_oe$2$(not in LMFDB)