Properties

Label 2.139.abo_zu
Base Field $\F_{139}$
Dimension $2$
Ordinary Yes
$p$-rank $2$
Principally polarizable Yes
Contains a Jacobian Yes

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Invariants

Base field:  $\F_{139}$
Dimension:  $2$
L-polynomial:  $1 - 40 x + 670 x^{2} - 5560 x^{3} + 19321 x^{4}$
Frobenius angles:  $\pm0.0805640498865$, $\pm0.240340054639$
Angle rank:  $2$ (numerical)
Number field:  4.0.145664.2
Galois group:  $D_{4}$
Jacobians:  70

This isogeny class is simple and geometrically 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 70 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 14392 368320064 7211797824952 139360343288800256 2692464149062492728952 52020874031128200684336704 1005095188920386768437331448952 19419444509983016085718854625280000 375203088409172540087081028301757622712 7249298872030389559333768265900052413258304

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 100 19062 2685340 373318926 51889074900 7212550105542 1002544346735500 139353666814409118 19370159740469887300 2692452204250953137302

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{139}$
The endomorphism algebra of this simple isogeny class is 4.0.145664.2.
All geometric endomorphisms are defined over $\F_{139}$.

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.bo_zu$2$(not in LMFDB)