Properties

Label 2.9.ah_bc
Base field F32\F_{3^{2}}
Dimension 22
pp-rank 22
Ordinary yes
Supersingular no
Simple no
Geometrically simple no
Primitive yes
Principally polarizable yes
Contains a Jacobian yes

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Invariants

Base field:  F32\F_{3^{2}}
Dimension:  22
L-polynomial:  (15x+9x2)(12x+9x2)( 1 - 5 x + 9 x^{2} )( 1 - 2 x + 9 x^{2} )
  17x+28x263x3+81x41 - 7 x + 28 x^{2} - 63 x^{3} + 81 x^{4}
Frobenius angles:  ±0.186429498677\pm0.186429498677, ±0.391826552031\pm0.391826552031
Angle rank:  22 (numerical)
Jacobians:  33
Isomorphism classes:  15

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

Newton polygon

This isogeny class is ordinary.

pp-rank:  22
Slopes:  [0,0,1,1][0, 0, 1, 1]

Point counts

Point counts of the abelian variety

rr 11 22 33 44 55
A(Fqr)A(\F_{q^r}) 4040 72007200 574240574240 4357440043574400 34862602003486260200

Point counts of the curve

rr 11 22 33 44 55 66 77 88 99 1010
C(Fqr)C(\F_{q^r}) 33 8989 786786 66416641 5904359043 532142532142 47885074788507 4305904143059041 387396354387396354 34865626493486562649

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 3 curves (of which all are hyperelliptic):

Decomposition and endomorphism algebra

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

Endomorphism algebra over F32\F_{3^{2}}
The isogeny class factors as 1.9.af ×\times 1.9.ac and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is:

Base change

This is a primitive isogeny class.

Twists

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

TwistExtension degreeCommon base change
2.9.ad_i222.81.h_cm
2.9.d_i222.81.h_cm
2.9.h_bc222.81.h_cm