Properties

Label 2.25.aq_eh
Base field F52\F_{5^{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:  F52\F_{5^{2}}
Dimension:  22
L-polynomial:  116x+111x2400x3+625x41 - 16 x + 111 x^{2} - 400 x^{3} + 625 x^{4}
Frobenius angles:  ±0.0738526172967\pm0.0738526172967, ±0.284366381360\pm0.284366381360
Angle rank:  22 (numerical)
Number field:  4.0.46224.1
Galois group:  D4D_{4}
Jacobians:  22
Isomorphism classes:  2

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}) 321321 370113370113 244628964244628964 152738602953152738602953 9535791612920195357916129201

Point counts of the curve

rr 11 22 33 44 55 66 77 88 99 1010
C(Fqr)C(\F_{q^r}) 1010 592592 1565815658 391012391012 97646509764650 244116214244116214 61033677706103367770 152587603012152587603012 38146999210183814699921018 9536746216715295367462167152

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 2 curves (of which all are hyperelliptic):

Decomposition and endomorphism algebra

All geometric endomorphisms are defined over F52\F_{5^{2}}.

Endomorphism algebra over F52\F_{5^{2}}
The endomorphism algebra of this simple isogeny class is 4.0.46224.1.

Base change

This is a primitive isogeny class.

Twists

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

TwistExtension degreeCommon base change
2.25.q_eh222.625.abi_bdr