Properties

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

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Invariants

Base field:  $\F_{73}$
Dimension:  $2$
L-polynomial:  $( 1 - 17 x + 73 x^{2} )( 1 - 15 x + 73 x^{2} )$
Frobenius angles:  $\pm0.0323195869136$, $\pm0.159004799845$
Angle rank:  $2$ (numerical)
Jacobians:  1

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 1 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 3363 27236937 150837168384 806307493291209 4297611830675103123 22902068002443410866176 122045027238992274935655651 650377878381822048892404086025 3465863710242070217007992518492416 18469587757765250116119549627771142377

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 42 5108 387738 28392868 2073064842 151334358158 11047399713882 806460090113476 58871586516205194 4297625826359864468

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{73}$
The isogeny class factors as 1.73.ar $\times$ 1.73.ap 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.ac_aef$2$(not in LMFDB)
2.73.c_aef$2$(not in LMFDB)
2.73.bg_pl$2$(not in LMFDB)
2.73.ai_bp$3$(not in LMFDB)
2.73.af_ae$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.73.ac_aef$2$(not in LMFDB)
2.73.c_aef$2$(not in LMFDB)
2.73.bg_pl$2$(not in LMFDB)
2.73.ai_bp$3$(not in LMFDB)
2.73.af_ae$3$(not in LMFDB)
2.73.az_lk$6$(not in LMFDB)
2.73.aw_jr$6$(not in LMFDB)
2.73.f_ae$6$(not in LMFDB)
2.73.i_bp$6$(not in LMFDB)
2.73.w_jr$6$(not in LMFDB)
2.73.z_lk$6$(not in LMFDB)