Properties

Label 2.139.abr_bck
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:  $( 1 - 23 x + 139 x^{2} )( 1 - 20 x + 139 x^{2} )$
Frobenius angles:  $\pm0.0707251543800$, $\pm0.177693164435$
Angle rank:  $2$ (numerical)
Jacobians:  12

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 12 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 14040 366163200 7206548862240 139353443025638400 2692463915889670408200 52020897823302827495731200 1005095255438196440674349305320 19419444612084003912333544680345600 375203088465633100831063443859455432480 7249298871840739210977088481874386779680000

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 97 18949 2683384 373300441 51889070407 7212553404262 1002544413084493 139353667547084401 19370159743384708936 2692452204180515360149

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{139}$
The isogeny class factors as 1.139.ax $\times$ 1.139.au 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.ad_aha$2$(not in LMFDB)
2.139.d_aha$2$(not in LMFDB)
2.139.br_bck$2$(not in LMFDB)
2.139.an_fi$3$(not in LMFDB)
2.139.ae_abq$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.139.ad_aha$2$(not in LMFDB)
2.139.d_aha$2$(not in LMFDB)
2.139.br_bck$2$(not in LMFDB)
2.139.an_fi$3$(not in LMFDB)
2.139.ae_abq$3$(not in LMFDB)
2.139.abk_xa$6$(not in LMFDB)
2.139.abb_qc$6$(not in LMFDB)
2.139.e_abq$6$(not in LMFDB)
2.139.n_fi$6$(not in LMFDB)
2.139.bb_qc$6$(not in LMFDB)
2.139.bk_xa$6$(not in LMFDB)