Properties

Label 2.4.ab_f
Base field F22\F_{2^{2}}
Dimension 22
pp-rank 22
Ordinary yes
Supersingular no
Simple yes
Geometrically simple yes
Primitive yes
Principally polarizable yes
Contains a Jacobian yes

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Invariants

Base field:  F22\F_{2^{2}}
Dimension:  22
L-polynomial:  1x+5x24x3+16x41 - x + 5 x^{2} - 4 x^{3} + 16 x^{4}
Frobenius angles:  ±0.304731991158\pm0.304731991158, ±0.605597892078\pm0.605597892078
Angle rank:  22 (numerical)
Number field:  4.0.2873.1
Galois group:  D4D_{4}
Jacobians:  33
Isomorphism classes:  3

This isogeny class is simple and geometrically 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}) 1717 459459 41484148 7022770227 11107971110797

Point counts of the curve

rr 11 22 33 44 55 66 77 88 99 1010
C(Fqr)C(\F_{q^r}) 44 2626 6767 274274 10841084 39353935 1596415964 6589065890 263011263011 10485861048586

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 F22\F_{2^{2}}.

Endomorphism algebra over F22\F_{2^{2}}
The endomorphism algebra of this simple isogeny class is 4.0.2873.1.

Base change

This is a primitive isogeny class.

Twists

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

TwistExtension degreeCommon base change
2.4.b_f222.16.j_bx