# Properties

 Label 2.73.abe_od 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: $( 1 - 17 x + 73 x^{2} )( 1 - 13 x + 73 x^{2} )$ 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:

• $y^2=17x^6+21x^5+6x^4+69x^3+25x^2+30x+56$
• $y^2=31x^6+26x^5+38x^4+35x^3+26x^2+37x+56$
• $y^2=22x^6+71x^5+68x^4+58x^3+7x^2+59x+31$
• $y^2=66x^6+69x^5+62x^4+62x^3+21x^2+18x+56$

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

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