Properties

Label 2.139.abn_yw
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:  $( 1 - 23 x + 139 x^{2} )( 1 - 16 x + 139 x^{2} )$
Frobenius angles:  $\pm0.0707251543800$, $\pm0.262608178953$
Angle rank:  $1$ (numerical)
Jacobians:  38

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 38 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 14508 368909424 7212548148624 139358818209873600 2692454812753783550148 52020850796219489993093376 1005095154221553703409927785908 19419444487837611884973222276422400 375203088447024628530509907710222277264 7249298872162111218021873908096346034366704

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 101 19093 2685620 373314841 51888894971 7212546884086 1002544312124729 139353666655494001 19370159742424031660 2692452204299875698853

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{139}$
The isogeny class factors as 1.139.ax $\times$ 1.139.aq and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is:
Endomorphism algebra over $\overline{\F}_{139}$
The base change of $A$ to $\F_{139^{6}}$ is 1.7212549413161.actyqc 2 and its endomorphism algebra is $\mathrm{M}_{2}($\(\Q(\sqrt{-3}) \)$)$
All geometric endomorphisms are defined over $\F_{139^{6}}$.
Remainder of endomorphism lattice by field

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.ah_adm$2$(not in LMFDB)
2.139.h_adm$2$(not in LMFDB)
2.139.bn_yw$2$(not in LMFDB)
2.139.abe_qx$3$(not in LMFDB)
2.139.aj_gk$3$(not in LMFDB)
2.139.a_ajr$3$(not in LMFDB)
2.139.a_w$3$(not in LMFDB)
2.139.a_iv$3$(not in LMFDB)
2.139.j_gk$3$(not in LMFDB)
2.139.be_qx$3$(not in LMFDB)
2.139.bn_yw$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.139.ah_adm$2$(not in LMFDB)
2.139.h_adm$2$(not in LMFDB)
2.139.bn_yw$2$(not in LMFDB)
2.139.abe_qx$3$(not in LMFDB)
2.139.aj_gk$3$(not in LMFDB)
2.139.a_ajr$3$(not in LMFDB)
2.139.a_w$3$(not in LMFDB)
2.139.a_iv$3$(not in LMFDB)
2.139.j_gk$3$(not in LMFDB)
2.139.be_qx$3$(not in LMFDB)
2.139.bn_yw$3$(not in LMFDB)
2.139.abu_bfb$6$(not in LMFDB)
2.139.abg_uo$6$(not in LMFDB)
2.139.ax_pa$6$(not in LMFDB)
2.139.aq_en$6$(not in LMFDB)
2.139.ao_mp$6$(not in LMFDB)
2.139.o_mp$6$(not in LMFDB)
2.139.q_en$6$(not in LMFDB)
2.139.x_pa$6$(not in LMFDB)
2.139.bg_uo$6$(not in LMFDB)
2.139.bu_bfb$6$(not in LMFDB)
2.139.a_aiv$12$(not in LMFDB)
2.139.a_aw$12$(not in LMFDB)
2.139.a_jr$12$(not in LMFDB)