Properties

Label 2.107.abj_tt
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:  $1 - 35 x + 513 x^{2} - 3745 x^{3} + 11449 x^{4}$
Frobenius angles:  $\pm0.0698121762543$, $\pm0.246087952504$
Angle rank:  $2$ (numerical)
Number field:  4.0.3556589.1
Galois group:  $D_{4}$
Jacobians:  $15$
Isomorphism classes:  15

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

$r$ $1$ $2$ $3$ $4$ $5$
$A(\F_{q^r})$ $8183$ $128824969$ $1500430027481$ $17182940904080861$ $196716107706164708368$

Point counts of the curve

$r$ $1$ $2$ $3$ $4$ $5$ $6$ $7$ $8$ $9$ $10$
$C(\F_{q^r})$ $73$ $11251$ $1224799$ $131087835$ $14025586608$ $1500729914647$ $160578130432429$ $17181861585333699$ $1838459211366428863$ $196715135741871505686$

Jacobians and polarizations

This isogeny class contains the Jacobians of 15 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 4.0.3556589.1.

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.bj_tt$2$(not in LMFDB)