Properties

Label 2.139.abp_bat
Base Field $\F_{139}$
Dimension $2$
Ordinary No
$p$-rank $1$
Principally polarizable Yes
Contains a Jacobian Yes

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Invariants

Base field:  $\F_{139}$
Dimension:  $2$
L-polynomial:  $1 - 41 x + 695 x^{2} - 5699 x^{3} + 19321 x^{4}$
Frobenius angles:  $\pm0.105232638034$, $\pm0.208549921524$
Angle rank:  $2$ (numerical)
Number field:  4.0.2043717.2
Galois group:  $D_{4}$
Jacobians:  16

This isogeny class is simple and geometrically simple.

Newton polygon

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

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
$A(\F_{q^r})$ 14277 367732689 7211121088383 139362633210982077 2692477571943557577072 52020911860186552938077049 1005095261623570755642251516091 19419444604298084873845806079577973 375203088457257006416193073378459527321 7249298871891215146456806633995387607561984

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 99 19031 2685087 373325059 51889333584 7212555350435 1002544419254169 139353667491212755 19370159742952286361 2692452204199262558486

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{139}$
The endomorphism algebra of this simple isogeny class is 4.0.2043717.2.
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.bp_bat$2$(not in LMFDB)