# Properties

 Label 2.73.abc_ne 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: $( 1 - 14 x + 73 x^{2} )^{2}$ Frobenius angles: $\pm0.194368965322$, $\pm0.194368965322$ Angle rank: $1$ (numerical) Jacobians: 29

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 29 curves, and hence is principally polarizable:

• $y^2=42x^6+41x^5+26x^4+12x^3+5x^2+4x+39$
• $y^2=9x^6+7x^5+39x^4+28x^3+26x^2+68x+27$
• $y^2=28x^6+46x^4+46x^2+28$
• $y^2=52x^6+x^5+64x^4+23x^3+36x^2+29x+34$
• $y^2=22x^6+37x^5+58x^4+47x^3+29x^2+64x+21$
• $y^2=34x^6+57x^4+57x^2+34$
• $y^2=15x^6+53x^5+22x^4+51x^3+68x^2+5x+5$
• $y^2=43x^6+12x^4+12x^2+43$
• $y^2=56x^6+15x^5+64x^4+21x^3+69x^2+30x+66$
• $y^2=7x^6+32x^5+69x^4+69x^3+42x^2+41x+32$
• $y^2=59x^6+59x^5+63x^4+68x^3+31x^2+22x+13$
• $y^2=39x^6+70x^5+31x^4+57x^3+58x^2+35x+20$
• $y^2=56x^6+20x^4+20x^2+56$
• $y^2=x^6+x^3+27$
• $y^2=50x^6+50x^4+50x^2+50$
• $y^2=2x^6+16x^5+14x^4+35x^3+14x^2+16x+2$
• $y^2=43x^6+13x^5+53x^4+24x^3+33x^2+52x+52$
• $y^2=43x^6+51x^5+45x^4+36x^3+15x^2+30x+7$
• $y^2=31x^6+7x^5+24x^4+30x^3+24x^2+7x+31$
• $y^2=10x^6+51x^5+62x^4+24x^3+62x^2+51x+10$
• $y^2=x^6+25x^3+3$
• $y^2=9x^6+66x^5+7x^4+8x^3+58x^2+41x+10$
• $y^2=15x^6+26x^5+x^4+8x^3+x^2+26x+15$
• $y^2=26x^6+42x^5+55x^4+58x^3+3x^2+62x+33$
• $y^2=x^6+37x^3+64$
• $y^2=20x^6+60x^5+4x^4+44x^3+55x^2+47x+39$
• $y^2=32x^6+44x^5+50x^4+35x^3+50x^2+44x+32$
• $y^2=53x^6+67x^5+69x^4+14x^3+18x^2+61x+34$
• $y^2=58x^6+48x^5+49x^4+28x^3+49x^2+48x+58$

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 3600 27878400 151585635600 806923560960000 4298001922141290000 22902252151718672409600 122045076333007799475171600 650377864081384538585333760000 3465863681233353401239556246787600 18469587737054229210488996280581760000

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 46 5230 389662 28414558 2073253006 151335574990 11047404157822 806460072381118 58871586023459566 4297625821540687150

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{73}$
 The isogeny class factors as 1.73.ao 2 and its endomorphism algebra is $\mathrm{M}_{2}($$$\Q(\sqrt{-6})$$$)$
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.a_aby $2$ (not in LMFDB) 2.73.bc_ne $2$ (not in LMFDB) 2.73.o_et $3$ (not in LMFDB)
Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 2.73.a_aby $2$ (not in LMFDB) 2.73.bc_ne $2$ (not in LMFDB) 2.73.o_et $3$ (not in LMFDB) 2.73.a_by $4$ (not in LMFDB) 2.73.ao_et $6$ (not in LMFDB)