Properties

Label 2.73.abf_ou
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:  $( 1 - 17 x + 73 x^{2} )( 1 - 14 x + 73 x^{2} )$
Frobenius angles:  $\pm0.0323195869136$, $\pm0.194368965322$
Angle rank:  $2$ (numerical)
Jacobians:  3

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 3 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 3420 27387360 150996953520 806413694486400 4297648897845359100 22902053537373714063360 122044989529565276509090620 650377840443461299253385100800 3465863683943557744642713623958960 18469587745198571841379435966667416800

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 43 5137 388150 28396609 2073082723 151334262574 11047396300459 806460043070401 58871586069495430 4297625823435766657

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{73}$
The isogeny class factors as 1.73.ar $\times$ 1.73.ao 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.ad_ado$2$(not in LMFDB)
2.73.d_ado$2$(not in LMFDB)
2.73.bf_ou$2$(not in LMFDB)
2.73.ah_bw$3$(not in LMFDB)
2.73.ae_g$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.73.ad_ado$2$(not in LMFDB)
2.73.d_ado$2$(not in LMFDB)
2.73.bf_ou$2$(not in LMFDB)
2.73.ah_bw$3$(not in LMFDB)
2.73.ae_g$3$(not in LMFDB)
2.73.ay_la$6$(not in LMFDB)
2.73.av_jk$6$(not in LMFDB)
2.73.e_g$6$(not in LMFDB)
2.73.h_bw$6$(not in LMFDB)
2.73.v_jk$6$(not in LMFDB)
2.73.y_la$6$(not in LMFDB)