Properties

Label 2.107.abi_ta
Base Field $\F_{107}$
Dimension $2$
Ordinary Yes
$p$-rank $2$
Principally polarizable Yes
Contains a Jacobian Yes

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Invariants

Base field:  $\F_{107}$
Dimension:  $2$
L-polynomial:  $( 1 - 20 x + 107 x^{2} )( 1 - 14 x + 107 x^{2} )$
Frobenius angles:  $\pm0.0823304377774$, $\pm0.263402699857$
Angle rank:  $2$ (numerical)
Jacobians:  20

This isogeny class is not simple.

Newton polygon

This isogeny class is ordinary.

$p$-rank:  $2$
Slopes:  $[0, 0, 1, 1]$

Point counts

This isogeny class contains the Jacobians of 20 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 8272 129175552 1500938294416 17183287418159104 196716031782848094352 2252190600390749948317696 25785338878827623582466059344 295216372758458844710307731865600 3379932277185452691706594731269500624 38696844631806666330693711679133023178752

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

Decomposition and endomorphism algebra

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:
All geometric endomorphisms are defined over $\F_{107}$.

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)