Properties

Label 2.107.abk_un
Base field $\F_{107}$
Dimension $2$
$p$-rank $2$
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:  $\F_{107}$
Dimension:  $2$
L-polynomial:  $1 - 36 x + 533 x^{2} - 3852 x^{3} + 11449 x^{4}$
Frobenius angles:  $\pm0.0666671800057$, $\pm0.224228209066$
Angle rank:  $2$ (numerical)
Number field:  4.0.1025.1
Galois group:  $D_{4}$
Jacobians:  $22$
Isomorphism classes:  22

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.

$p$-rank:  $2$
Slopes:  $[0, 0, 1, 1]$

Point counts

Point counts of the abelian variety

$r$ $1$ $2$ $3$ $4$ $5$
$A(\F_{q^r})$ $8095$ $128475745$ $1499936926720$ $17182698802220025$ $196716559096562407375$

Point counts of the curve

$r$ $1$ $2$ $3$ $4$ $5$ $6$ $7$ $8$ $9$ $10$
$C(\F_{q^r})$ $72$ $11220$ $1224396$ $131085988$ $14025618792$ $1500730738710$ $160578139501656$ $17181861616663108$ $1838459210550747732$ $196715135722672310100$

Jacobians and polarizations

This isogeny class contains the Jacobians of 22 curves (of which all are hyperelliptic), and hence is principally polarizable:

Decomposition and endomorphism algebra

All geometric endomorphisms are defined over $\F_{107}$.

Endomorphism algebra over $\F_{107}$
The endomorphism algebra of this simple isogeny class is 4.0.1025.1.

Base change

This is a primitive isogeny class.

Twists

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

TwistExtension degreeCommon base change
2.107.bk_un$2$(not in LMFDB)