Properties

Label 2.139.abo_zt
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:  $( 1 - 23 x + 139 x^{2} )( 1 - 17 x + 139 x^{2} )$
Frobenius angles:  $\pm0.0707251543800$, $\pm0.243700857809$
Angle rank:  $2$ (numerical)
Jacobians:  20

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 20 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 14391 368280081 7211474931024 139358953709309529 2692459997933940632151 52020864505831010897592576 1005095171424143328920258194431 19419444483958775435838570013831209 375203088377917546895061526843844022864 7249298871999371988678641492275598205006801

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 100 19060 2685220 373315204 51888994900 7212548784886 1002544329283660 139353666627659524 19370159738856323260 2692452204239432943700

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{139}$
The isogeny class factors as 1.139.ax $\times$ 1.139.ar 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 are some of the twists of this isogeny class.
TwistExtension DegreeCommon base change
2.139.ag_aej$2$(not in LMFDB)
2.139.g_aej$2$(not in LMFDB)
2.139.bo_zt$2$(not in LMFDB)
2.139.ak_gd$3$(not in LMFDB)
2.139.ab_g$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.139.ag_aej$2$(not in LMFDB)
2.139.g_aej$2$(not in LMFDB)
2.139.bo_zt$2$(not in LMFDB)
2.139.ak_gd$3$(not in LMFDB)
2.139.ab_g$3$(not in LMFDB)
2.139.abh_ve$6$(not in LMFDB)
2.139.ay_ph$6$(not in LMFDB)
2.139.b_g$6$(not in LMFDB)
2.139.k_gd$6$(not in LMFDB)
2.139.y_ph$6$(not in LMFDB)
2.139.bh_ve$6$(not in LMFDB)