Properties

Label 2.139.abo_bab
Base field $\F_{139}$
Dimension $2$
$p$-rank $2$
Ordinary yes
Supersingular no
Simple no
Geometrically simple no
Primitive yes
Principally polarizable yes
Contains a Jacobian yes

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Invariants

Base field:  $\F_{139}$
Dimension:  $2$
L-polynomial:  $( 1 - 21 x + 139 x^{2} )( 1 - 19 x + 139 x^{2} )$
  $1 - 40 x + 677 x^{2} - 5560 x^{3} + 19321 x^{4}$
Frobenius angles:  $\pm0.150285916016$, $\pm0.201746658314$
Angle rank:  $2$ (numerical)
Jacobians:  $24$

This isogeny class is not 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

$r$ $1$ $2$ $3$ $4$ $5$
$A(\F_{q^r})$ $14399$ $368600001$ $7214058195344$ $139370028633106425$ $2692492625858105380079$

Point counts of the curve

$r$ $1$ $2$ $3$ $4$ $5$ $6$ $7$ $8$ $9$ $10$
$C(\F_{q^r})$ $100$ $19076$ $2686180$ $373344868$ $51889623700$ $7212558769526$ $1002544448153740$ $139353667550877508$ $19370159738988717820$ $2692452204092386759556$

Jacobians and polarizations

This isogeny class contains the Jacobians of 24 curves (of which all are hyperelliptic), and hence is principally polarizable:

Decomposition and endomorphism algebra

All geometric endomorphisms are defined over $\F_{139}$.

Endomorphism algebra over $\F_{139}$
The isogeny class factors as 1.139.av $\times$ 1.139.at and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is:

Base change

This is a primitive isogeny class.

Twists

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

TwistExtension degreeCommon base change
2.139.ac_aer$2$(not in LMFDB)
2.139.c_aer$2$(not in LMFDB)
2.139.bo_bab$2$(not in LMFDB)