Properties

Label 2.73.abe_od
Base Field $\F_{73}$
Dimension $2$
Ordinary Yes
$p$-rank $2$
Principally polarizable Yes
Contains a Jacobian Yes

Learn more about

Invariants

Base field:  $\F_{73}$
Dimension:  $2$
L-polynomial:  $( 1 - 17 x + 73 x^{2} )( 1 - 13 x + 73 x^{2} )$
Frobenius angles:  $\pm0.0323195869136$, $\pm0.224822766824$
Angle rank:  $2$ (numerical)
Jacobians:  4

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 4 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 3477 27527409 151124161104 806469648123321 4297635466930080957 22902005289804450840576 122044941517692634202858493 650377811375675641758277332009 3465863675610050614610750964933456 18469587750069461875975782994144276449

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 44 5164 388478 28398580 2073076244 151333943758 11047391954468 806460007026724 58871585927941454 4297625824569157564

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{73}$
The isogeny class factors as 1.73.ar $\times$ 1.73.an 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 $\F_{73}$.

Base change

This is a primitive isogeny class.

Twists

Below are some of the twists of this isogeny class.
TwistExtension DegreeCommon base change
2.73.ae_acx$2$(not in LMFDB)
2.73.e_acx$2$(not in LMFDB)
2.73.be_od$2$(not in LMFDB)
2.73.ag_cd$3$(not in LMFDB)
2.73.ad_q$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.73.ae_acx$2$(not in LMFDB)
2.73.e_acx$2$(not in LMFDB)
2.73.be_od$2$(not in LMFDB)
2.73.ag_cd$3$(not in LMFDB)
2.73.ad_q$3$(not in LMFDB)
2.73.ax_kq$6$(not in LMFDB)
2.73.au_jd$6$(not in LMFDB)
2.73.d_q$6$(not in LMFDB)
2.73.g_cd$6$(not in LMFDB)
2.73.u_jd$6$(not in LMFDB)
2.73.x_kq$6$(not in LMFDB)