Properties

Label 2.107.abi_ta
Base field $\F_{107}$
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:  $\F_{107}$
Dimension:  $2$
L-polynomial:  $( 1 - 20 x + 107 x^{2} )( 1 - 14 x + 107 x^{2} )$
  $1 - 34 x + 494 x^{2} - 3638 x^{3} + 11449 x^{4}$
Frobenius angles:  $\pm0.0823304377774$, $\pm0.263402699857$
Angle rank:  $2$ (numerical)
Jacobians:  $20$
Isomorphism classes:  80

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

$r$ $1$ $2$ $3$ $4$ $5$
$A(\F_{q^r})$ $8272$ $129175552$ $1500938294416$ $17183287418159104$ $196716031782848094352$

Point counts of the curve

$r$ $1$ $2$ $3$ $4$ $5$ $6$ $7$ $8$ $9$ $10$
$C(\F_{q^r})$ $74$ $11282$ $1225214$ $131090478$ $14025581194$ $1500729693122$ $160578131311966$ $17181861676208926$ $1838459213210445578$ $196715135764260757682$

Jacobians and polarizations

This isogeny class contains the Jacobians of 20 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 isogeny class factors as 1.107.au $\times$ 1.107.ao 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
2.107.ag_aco$2$(not in LMFDB)
2.107.g_aco$2$(not in LMFDB)
2.107.bi_ta$2$(not in LMFDB)