Properties

Label 2.139.abq_bbn
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:  $( 1 - 23 x + 139 x^{2} )( 1 - 19 x + 139 x^{2} )$
Frobenius angles:  $\pm0.0707251543800$, $\pm0.201746658314$
Angle rank:  $2$ (numerical)
Jacobians:  32

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 32 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 14157 366906969 7208491386096 139356427372718985 2692465343398114418277 52020890491776484612029696 1005095226972862984133803001517 19419444550237390786724254964542665 375203088375214777213507315953290778096 7249298871775310552130533113434718432540329

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 98 18988 2684108 373308436 51889097918 7212552387766 1002544384691402 139353667103273956 19370159738716790612 2692452204156214591228

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{139}$
The isogeny class factors as 1.139.ax $\times$ 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 are some of the twists of this isogeny class.
TwistExtension DegreeCommon base change
2.139.ae_agd$2$(not in LMFDB)
2.139.e_agd$2$(not in LMFDB)
2.139.bq_bbn$2$(not in LMFDB)
2.139.am_fp$3$(not in LMFDB)
2.139.ad_aba$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.139.ae_agd$2$(not in LMFDB)
2.139.e_agd$2$(not in LMFDB)
2.139.bq_bbn$2$(not in LMFDB)
2.139.am_fp$3$(not in LMFDB)
2.139.ad_aba$3$(not in LMFDB)
2.139.abj_wk$6$(not in LMFDB)
2.139.aba_pv$6$(not in LMFDB)
2.139.d_aba$6$(not in LMFDB)
2.139.m_fp$6$(not in LMFDB)
2.139.ba_pv$6$(not in LMFDB)
2.139.bj_wk$6$(not in LMFDB)