# Properties

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

# Learn more about

## Invariants

 Base field: $\F_{73}$ Dimension: $2$ L-polynomial: $( 1 - 17 x + 73 x^{2} )( 1 - 11 x + 73 x^{2} )$ Frobenius angles: $\pm0.0323195869136$, $\pm0.277387524567$ Angle rank: $2$ (numerical) Jacobians: 13

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 13 curves, and hence is principally polarizable:

• $y^2=20x^6+18x^5+7x^4+36x^3+15x^2+9x+7$
• $y^2=47x^6+5x^5+10x^4+39x^3+12x+19$
• $y^2=42x^6+56x^5+60x^4+13x^3+69x^2+70x+56$
• $y^2=40x^6+63x^5+2x^4+10x^3+2x^2+63x+40$
• $y^2=48x^6+38x^5+58x^4+47x^3+58x^2+38x+48$
• $y^2=20x^6+10x^5+54x^4+26x^3+8x^2+58x+14$
• $y^2=54x^6+64x^5+15x^4+16x^3+19x^2+42x+45$
• $y^2=x^6+49x^5+57x^4+67x^3+28x^2+67x+41$
• $y^2=28x^6+24x^5+12x^4+12x^3+25x^2+34$
• $y^2=58x^6+32x^5+72x^4+31x^3+72x^2+32x+58$
• $y^2=32x^6+27x^5+42x^4+39x^3+42x^2+27x+32$
• $y^2=25x^6+25x^5+44x^4+60x^3+61x^2+60x+71$
• $y^2=52x^6+70x^5+19x^4+38x^3+19x^2+70x+52$

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 3591 27776385 151290151488 806466922832025 4297526514615651471 22901893365903937781760 122044886172924763129313967 650377812936621009927456376425 3465863703786211109133699353458752 18469587776247426631825842836030449425

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 46 5212 388906 28398484 2073023686 151333204174 11047386944710 806460008962276 58871586406545178 4297625830660419532

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{73}$
 The isogeny class factors as 1.73.ar $\times$ 1.73.al 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.ag_abp $2$ (not in LMFDB) 2.73.g_abp $2$ (not in LMFDB) 2.73.bc_mv $2$ (not in LMFDB) 2.73.ae_cr $3$ (not in LMFDB) 2.73.ab_bk $3$ (not in LMFDB)
Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 2.73.ag_abp $2$ (not in LMFDB) 2.73.g_abp $2$ (not in LMFDB) 2.73.bc_mv $2$ (not in LMFDB) 2.73.ae_cr $3$ (not in LMFDB) 2.73.ab_bk $3$ (not in LMFDB) 2.73.av_jw $6$ (not in LMFDB) 2.73.as_ip $6$ (not in LMFDB) 2.73.b_bk $6$ (not in LMFDB) 2.73.e_cr $6$ (not in LMFDB) 2.73.s_ip $6$ (not in LMFDB) 2.73.v_jw $6$ (not in LMFDB)