Properties

Label 1.9.f
Base field F32\F_{3^{2}}
Dimension 11
pp-rank 11
Ordinary yes
Supersingular no
Simple yes
Geometrically simple yes
Primitive no
Principally polarizable yes
Contains a Jacobian yes

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Invariants

Base field:  F32\F_{3^{2}}
Dimension:  11
L-polynomial:  1+5x+9x21 + 5 x + 9 x^{2}
Frobenius angles:  ±0.813570501323\pm0.813570501323
Angle rank:  11 (numerical)
Number field:  Q(11)\Q(\sqrt{-11})
Galois group:  C2C_2
Jacobians:  11
Isomorphism classes:  1

This isogeny class is simple and geometrically simple, not primitive, ordinary, and not supersingular. It is principally polarizable and contains a Jacobian.

Newton polygon

This isogeny class is ordinary.

pp-rank:  11
Slopes:  [0,1][0, 1]

Point counts

Point counts of the abelian variety

rr 11 22 33 44 55
A(Fqr)A(\F_{q^r}) 1515 7575 720720 66756675 5857558575

Point counts of the curve

rr 11 22 33 44 55 66 77 88 99 1010
C(Fqr)C(\F_{q^r}) 1515 7575 720720 66756675 5857558575 532800532800 47804554780455 4304707543047075 387441360387441360 34866768753486676875

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobian of 1 curve (which is hyperelliptic):

Decomposition and endomorphism algebra

All geometric endomorphisms are defined over F32\F_{3^{2}}.

Endomorphism algebra over F32\F_{3^{2}}
The endomorphism algebra of this simple isogeny class is Q(11)\Q(\sqrt{-11}) .

Base change

This isogeny class is not primitive. It is a base change from the following isogeny classes over subfields of F32\F_{3^{2}}.

SubfieldPrimitive Model
F3\F_{3}1.3.ab
F3\F_{3}1.3.b

Twists

Below is a list of all twists of this isogeny class.

TwistExtension degreeCommon base change
1.9.af221.81.ah