Properties

Label 2.193.abw_bla
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:  $( 1 - 24 x + 193 x^{2} )^{2}$
Frobenius angles:  $\pm0.168091317575$, $\pm0.168091317575$
Angle rank:  $1$ (numerical)
Jacobians:  34

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 34 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 28900 1373443600 51683590156900 1925229510696960000 71709390988296636422500 2671086483284152145855952400 99495248463399037299797226172900 3706098388862990664067605070479360000 138048458699079064512721462633179600316900 5142167038083624773322742904199738441034090000

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 146 36870 7189202 1387564798 267786999506 51682569295110 9974730665550482 1925122955520115198 371548729910257442066 71708904872702398969350

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{193}$
The isogeny class factors as 1.193.ay 2 and its endomorphism algebra is $\mathrm{M}_{2}($\(\Q(\sqrt{-1}) \)$)$
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.a_ahi$2$(not in LMFDB)
2.193.bw_bla$2$(not in LMFDB)
2.193.y_ot$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.193.a_ahi$2$(not in LMFDB)
2.193.bw_bla$2$(not in LMFDB)
2.193.y_ot$3$(not in LMFDB)
2.193.abm_bbu$4$(not in LMFDB)
2.193.abc_wk$4$(not in LMFDB)
2.193.ak_by$4$(not in LMFDB)
2.193.a_hi$4$(not in LMFDB)
2.193.k_by$4$(not in LMFDB)
2.193.bc_wk$4$(not in LMFDB)
2.193.bm_bbu$4$(not in LMFDB)
2.193.ay_ot$6$(not in LMFDB)
2.193.a_amy$8$(not in LMFDB)
2.193.a_my$8$(not in LMFDB)
2.193.ao_d$12$(not in LMFDB)
2.193.o_d$12$(not in LMFDB)