Properties

Label 2.139.abo_bab
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:  $( 1 - 21 x + 139 x^{2} )( 1 - 19 x + 139 x^{2} )$
Frobenius angles:  $\pm0.150285916016$, $\pm0.201746658314$
Angle rank:  $2$ (numerical)
Jacobians:  24

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 24 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 14399 368600001 7214058195344 139370028633106425 2692492625858105380079 52020936520562880739604736 1005095290596673647585925220279 19419444612612587097783922618888425 375203088380482050668775137130713868944 7249298871603457166062759364598553684646241

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 100 19076 2686180 373344868 51889623700 7212558769526 1002544448153740 139353667550877508 19370159738988717820 2692452204092386759556

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{139}$
The isogeny class factors as 1.139.av $\times$ 1.139.at 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 $\F_{139}$.

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.ac_aer$2$(not in LMFDB)
2.139.c_aer$2$(not in LMFDB)
2.139.bo_bab$2$(not in LMFDB)