Properties

Label 2.131.abn_yq
Base field $\F_{131}$
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:  $\F_{131}$
Dimension:  $2$
L-polynomial:  $( 1 - 21 x + 131 x^{2} )( 1 - 18 x + 131 x^{2} )$
  $1 - 39 x + 640 x^{2} - 5109 x^{3} + 17161 x^{4}$
Frobenius angles:  $\pm0.130292526609$, $\pm0.211976702993$
Angle rank:  $2$ (numerical)
Jacobians:  $21$

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

$r$ $1$ $2$ $3$ $4$ $5$
$A(\F_{q^r})$ $12654$ $290409300$ $5054442442056$ $86739851650471200$ $1488398852121016833954$

Point counts of the curve

$r$ $1$ $2$ $3$ $4$ $5$ $6$ $7$ $8$ $9$ $10$
$C(\F_{q^r})$ $93$ $16921$ $2248326$ $294532681$ $38580055503$ $5053919578018$ $662062674021933$ $86730203712894481$ $11361656653753329666$ $1488377021704632064201$

Jacobians and polarizations

This isogeny class contains the Jacobians of 21 curves (of which all are hyperelliptic), and hence is principally polarizable:

Decomposition and endomorphism algebra

All geometric endomorphisms are defined over $\F_{131}$.

Endomorphism algebra over $\F_{131}$
The isogeny class factors as 1.131.av $\times$ 1.131.as 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
2.131.ad_aem$2$(not in LMFDB)
2.131.d_aem$2$(not in LMFDB)
2.131.bn_yq$2$(not in LMFDB)