Properties

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

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 2 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 13689 363703041 7198725105936 139335482071482489 2692431221219247245049 52020850796219489993093376 1005095208705385769683771727889 19419444608054130384362092232563689 375203088588841496470422251715249251856 7249298872223650072661018639268040192724001

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 94 18820 2680468 373252324 51888440314 7212546884086 1002544366470286 139353667518166084 19370159749745440972 2692452204322731760900

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{139}$
The isogeny class factors as 1.139.ax 2 and its endomorphism algebra is $\mathrm{M}_{2}($\(\Q(\sqrt{-3}) \)$)$
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.a_ajr$2$(not in LMFDB)
2.139.bu_bfb$2$(not in LMFDB)
2.139.aq_en$3$(not in LMFDB)
2.139.ah_adm$3$(not in LMFDB)
2.139.o_mp$3$(not in LMFDB)
2.139.x_pa$3$(not in LMFDB)
2.139.bg_uo$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.139.a_ajr$2$(not in LMFDB)
2.139.bu_bfb$2$(not in LMFDB)
2.139.aq_en$3$(not in LMFDB)
2.139.ah_adm$3$(not in LMFDB)
2.139.o_mp$3$(not in LMFDB)
2.139.x_pa$3$(not in LMFDB)
2.139.bg_uo$3$(not in LMFDB)
2.139.a_jr$4$(not in LMFDB)
2.139.abn_yw$6$(not in LMFDB)
2.139.abg_uo$6$(not in LMFDB)
2.139.abe_qx$6$(not in LMFDB)
2.139.ax_pa$6$(not in LMFDB)
2.139.ao_mp$6$(not in LMFDB)
2.139.aj_gk$6$(not in LMFDB)
2.139.a_w$6$(not in LMFDB)
2.139.a_iv$6$(not in LMFDB)
2.139.h_adm$6$(not in LMFDB)
2.139.j_gk$6$(not in LMFDB)
2.139.q_en$6$(not in LMFDB)
2.139.be_qx$6$(not in LMFDB)
2.139.bn_yw$6$(not in LMFDB)
2.139.a_aiv$12$(not in LMFDB)
2.139.a_aw$12$(not in LMFDB)