Properties

Label 2.193.abx_blw
Base Field $\F_{193}$
Dimension $2$
Ordinary Yes
$p$-rank $2$
Principally polarizable Yes
Contains a Jacobian Yes

Learn more about

Invariants

Base field:  $\F_{193}$
Dimension:  $2$
L-polynomial:  $( 1 - 26 x + 193 x^{2} )( 1 - 23 x + 193 x^{2} )$
Frobenius angles:  $\pm0.114714697559$, $\pm0.189598946136$
Angle rank:  $2$ (numerical)
Jacobians:  27

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 27 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 28728 1371474720 51672688639488 1925184624854198400 71709241820388123337848 2671086086743762700997304320 99495247728717993520377015693624 3706098388738473715164153559172620800 138048458705831895461863912322255133015552 5142167038122968781748062131813480701083693600

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 145 36817 7187686 1387532449 267786442465 51682561622494 9974730591896257 1925122955455435201 371548729928432261158 71708904873251061767857

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{193}$
The isogeny class factors as 1.193.aba $\times$ 1.193.ax 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 $\F_{193}$.

Base change

This is a primitive isogeny class.

Twists

Below are some of the twists of this isogeny class.
TwistExtension DegreeCommon base change
2.193.ad_aie$2$(not in LMFDB)
2.193.d_aie$2$(not in LMFDB)
2.193.bx_blw$2$(not in LMFDB)
2.193.abc_qw$3$(not in LMFDB)
2.193.ab_ake$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.193.ad_aie$2$(not in LMFDB)
2.193.d_aie$2$(not in LMFDB)
2.193.bx_blw$2$(not in LMFDB)
2.193.abc_qw$3$(not in LMFDB)
2.193.ab_ake$3$(not in LMFDB)
2.193.abz_bnw$6$(not in LMFDB)
2.193.ay_mw$6$(not in LMFDB)
2.193.b_ake$6$(not in LMFDB)
2.193.y_mw$6$(not in LMFDB)
2.193.bc_qw$6$(not in LMFDB)
2.193.bz_bnw$6$(not in LMFDB)