Properties

Label 1.7.d
Base field F7\F_{7}
Dimension 11
pp-rank 11
Ordinary yes
Supersingular no
Simple yes
Geometrically simple yes
Primitive yes
Principally polarizable yes
Contains a Jacobian yes

Related objects

Downloads

Learn more

Invariants

Base field:  F7\F_{7}
Dimension:  11
L-polynomial:  1+3x+7x21 + 3 x + 7 x^{2}
Frobenius angles:  ±0.691875465479\pm0.691875465479
Angle rank:  11 (numerical)
Number field:  Q(19)\Q(\sqrt{-19})
Galois group:  C2C_2
Jacobians:  11
Isomorphism classes:  1

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:  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}) 1111 5555 308308 24752475 1684116841

Point counts of the curve

rr 11 22 33 44 55 66 77 88 99 1010
C(Fqr)C(\F_{q^r}) 1111 5555 308308 24752475 1684116841 117040117040 825143825143 57642755764275 4034399640343996 282507775282507775

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 F7\F_{7}.

Endomorphism algebra over F7\F_{7}
The endomorphism algebra of this simple isogeny class is Q(19)\Q(\sqrt{-19}) .

Base change

This is a primitive isogeny class.

Twists

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

TwistExtension degreeCommon base change
1.7.ad221.49.f