Properties

Label 2.139.abo_zv
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:  $1 - 40 x + 671 x^{2} - 5560 x^{3} + 19321 x^{4}$
Frobenius angles:  $\pm0.0898857305018$, $\pm0.236719804447$
Angle rank:  $2$ (numerical)
Number field:  4.0.8624784.2
Galois group:  $D_{4}$
Jacobians:  16

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 16 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 14393 368360049 7212120722900 139361731378539849 2692468279437281892353 52020883406693485687770000 1005095205670496742378392964233 19419444533132715580844133381226569 375203088431356050483559246789623322100 7249298872037169387692663690625155469516609

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 100 19064 2685460 373322644 51889154500 7212551405438 1002544363443100 139353666980531044 19370159741615128780 2692452204253471224104

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{139}$
The endomorphism algebra of this simple isogeny class is 4.0.8624784.2.
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_zv$2$(not in LMFDB)