# Properties

 Label 2.73.abc_na 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: $( 1 - 16 x + 73 x^{2} )( 1 - 12 x + 73 x^{2} )$ Frobenius angles: $\pm0.114200251220$, $\pm0.252180272892$ Angle rank: $2$ (numerical) Jacobians: 20

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 20 curves, and hence is principally polarizable:

• $y^2=23x^6+52x^5+34x^4+25x^3+54x^2+53x+19$
• $y^2=61x^6+12x^5+37x^4+2x^3+24x^2+54x+36$
• $y^2=7x^6+61x^5+21x^4+12x^3+40x^2+42x+43$
• $y^2=54x^6+45x^5+21x^4+41x^3+46x^2+37x+11$
• $y^2=11x^6+2x^5+9x^4+31x^3+9x^2+2x+11$
• $y^2=26x^6+x^5+30x^4+57x^3+36x^2+55x+64$
• $y^2=21x^6+44x^5+31x^4+21x^3+31x^2+44x+21$
• $y^2=61x^6+26x^5+8x^4+46x^3+55x^2+13x+50$
• $y^2=60x^6+32x^5+2x^4+22x^3+35x^2+18x+34$
• $y^2=11x^6+35x^5+20x^4+27x^3+65x^2+38x+62$
• $y^2=10x^6+28x^5+11x^4+67x^3+30x^2+14x+7$
• $y^2=62x^6+19x^5+x^4+27x^3+x^2+19x+62$
• $y^2=39x^6+35x^5+36x^4+49x^3+68x^2+11x+5$
• $y^2=39x^6+62x^5+20x^4+31x^3+40x^2+72x+13$
• $y^2=37x^6+45x^5+29x^4+42x^3+61x^2+66x+41$
• $y^2=41x^6+47x^5+22x^4+47x^3+22x^2+47x+41$
• $y^2=27x^6+36x^5+30x^4+12x^3+27x^2+11x+7$
• $y^2=39x^6+70x^5+63x^4+67x^3+45x^2+67x+14$
• $y^2=47x^6+67x^5+3x^4+42x^3+23x^2+31x+37$
• $y^2=28x^6+25x^5+48x^4+x^3+48x^2+25x+28$

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 3596 27833040 151454289068 806721737932800 4297796432309223596 22902107915204516690640 122045019013413640032761612 650377878209633108279564697600 3465863731090637397489247831019852 18469587789429404773790391526386133200

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 46 5222 389326 28407454 2073153886 151334621894 11047398969310 806460089899966 58871586870341518 4297625833727689382

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{73}$
 The isogeny class factors as 1.73.aq $\times$ 1.73.am 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_abu $2$ (not in LMFDB) 2.73.e_abu $2$ (not in LMFDB) 2.73.bc_na $2$ (not in LMFDB)
Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 2.73.ae_abu $2$ (not in LMFDB) 2.73.e_abu $2$ (not in LMFDB) 2.73.bc_na $2$ (not in LMFDB) 2.73.as_ik $4$ (not in LMFDB) 2.73.ag_cw $4$ (not in LMFDB) 2.73.g_cw $4$ (not in LMFDB) 2.73.s_ik $4$ (not in LMFDB)