# Properties

 Label 2.73.abc_nd 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: $( 1 - 15 x + 73 x^{2} )( 1 - 13 x + 73 x^{2} )$ Frobenius angles: $\pm0.159004799845$, $\pm0.224822766824$ Angle rank: $2$ (numerical) Jacobians: 6

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 6 curves, and hence is principally polarizable:

• $y^2=35x^6+6x^5+6x^4+17x^3+6x^2+6x+35$
• $y^2=70x^6+17x^5+27x^4+8x^3+27x^2+17x+70$
• $y^2=11x^6+68x^5+43x^4+30x^3+43x^2+68x+11$
• $y^2=15x^6+50x^5+37x^4+71x^3+37x^2+50x+15$
• $y^2=65x^6+51x^5+67x^4+19x^3+67x^2+51x+65$
• $y^2=62x^6+70x^5+55x^4+41x^3+55x^2+70x+62$

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 3599 27867057 151552795904 806873274258489 4297951420023512999 22902218368895659032576 122045066030539993364569127 650377872951958257524086538025 3465863699198358666291218914893056 18469587754491797515450339119962847777

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 46 5228 389578 28412788 2073228646 151335351758 11047403225254 806460083380516 58871586328615354 4297625825598175868

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{73}$
 The isogeny class factors as 1.73.ap $\times$ 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 is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 2.73.ac_abx $2$ (not in LMFDB) 2.73.c_abx $2$ (not in LMFDB) 2.73.bc_nd $2$ (not in LMFDB)