Properties

Label 2.139.abp_baq
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:  $( 1 - 23 x + 139 x^{2} )( 1 - 18 x + 139 x^{2} )$
Frobenius angles:  $\pm0.0707251543800$, $\pm0.223543330897$
Angle rank:  $2$ (numerical)
Jacobians:  8

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 8 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 14274 367612596 7210128042936 139358209022326944 2692463754100883071374 52020878445522817743197376 1005095196851466588777575558334 19419444504822634411935927814360704 375203088347549871681192507667165304856 7249298871847897532620977595416190369279476

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 99 19025 2684718 373313209 51889067289 7212550717586 1002544354646451 139353666777378289 19370159737288567722 2692452204183174022625

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{139}$
The isogeny class factors as 1.139.ax $\times$ 1.139.as 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.af_afg$2$(not in LMFDB)
2.139.f_afg$2$(not in LMFDB)
2.139.bp_baq$2$(not in LMFDB)
2.139.al_fw$3$(not in LMFDB)
2.139.ac_ak$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.139.af_afg$2$(not in LMFDB)
2.139.f_afg$2$(not in LMFDB)
2.139.bp_baq$2$(not in LMFDB)
2.139.al_fw$3$(not in LMFDB)
2.139.ac_ak$3$(not in LMFDB)
2.139.abi_vu$6$(not in LMFDB)
2.139.az_po$6$(not in LMFDB)
2.139.c_ak$6$(not in LMFDB)
2.139.l_fw$6$(not in LMFDB)
2.139.z_po$6$(not in LMFDB)
2.139.bi_vu$6$(not in LMFDB)