Properties

Label 2.139.abq_bbl
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:  $1 - 42 x + 713 x^{2} - 5838 x^{3} + 19321 x^{4}$
Frobenius angles:  $\pm0.0334610337581$, $\pm0.211779178183$
Angle rank:  $2$ (numerical)
Number field:  4.0.747072.3
Galois group:  $D_{4}$
Jacobians:  6

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 6 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 14155 366826825 7207813138180 139353291208532025 2692454991489202493275 52020863308360140625517200 1005095167106587555774194582115 19419444436356303288955931865141225 375203088184181290978693277509237940260 7249298871485724345335165351180569967595625

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 98 18984 2683856 373300036 51888898418 7212548618862 1002544324977062 139353666286064836 19370159728854533984 2692452204048659773224

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{139}$
The endomorphism algebra of this simple isogeny class is 4.0.747072.3.
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.bq_bbl$2$(not in LMFDB)