Properties

Label 2.139.abn_yx
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:  $1 - 39 x + 647 x^{2} - 5421 x^{3} + 19321 x^{4}$
Frobenius angles:  $\pm0.0791680831941$, $\pm0.259916372902$
Angle rank:  $2$ (numerical)
Number field:  4.0.248725.1
Galois group:  $D_{4}$
Jacobians:  33

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 33 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 14509 368949361 7212862927831 139360124139480189 2692458526190717697424 52020858799587705005653081 1005095167881651190310169549379 19419444506838419916872377305762549 375203088470093745017904891805700965201 7249298872192292385118889503411928078354176

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 101 19095 2685737 373318339 51888966536 7212547993731 1002544325750159 139353666791843539 19370159743614993263 2692452204311085244950

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{139}$
The endomorphism algebra of this simple isogeny class is 4.0.248725.1.
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.bn_yx$2$(not in LMFDB)