Properties

Label 2.107.abk_uq
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:  $1 - 36 x + 536 x^{2} - 3852 x^{3} + 11449 x^{4}$
Frobenius angles:  $\pm0.112288198128$, $\pm0.203926913540$
Angle rank:  $2$ (numerical)
Number field:  4.0.499968.5
Galois group:  $D_{4}$
Jacobians:  $8$
Isomorphism classes:  8

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

$r$ $1$ $2$ $3$ $4$ $5$
$A(\F_{q^r})$ $8098$ $128547652$ $1500335061106$ $17183896870412304$ $196719088775649102178$

Point counts of the curve

$r$ $1$ $2$ $3$ $4$ $5$ $6$ $7$ $8$ $9$ $10$
$C(\F_{q^r})$ $72$ $11226$ $1224720$ $131095126$ $14025799152$ $1500733493898$ $160578173201112$ $17181861942027934$ $1838459212773454152$ $196715135727105319866$

Jacobians and polarizations

This isogeny class contains the Jacobians of 8 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 4.0.499968.5.

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_uq$2$(not in LMFDB)