# Properties

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

## 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:

• $y^2=63x^6+62x^5+56x^4+68x^3+53x^2+21x+71$
• $y^2=34x^6+53x^5+24x^4+37x^3+56x^2+6x+62$
• $y^2=42x^6+25x^5+30x^4+14x^3+44x^2+15x+11$

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

 $r$ 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.
 Twist Extension Degree Common 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.
 Twist Extension Degree Common 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)