# Properties

 Label 2.73.abc_mz 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: $1 - 28 x + 337 x^{2} - 2044 x^{3} + 5329 x^{4}$ Frobenius angles: $\pm0.100935715044$, $\pm0.258299334338$ Angle rank: $2$ (numerical) Number field: 4.0.109025.1 Galois group: $D_{4}$ Jacobians: 20

This isogeny class is simple and geometrically 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:

• $y^2=72x^6+50x^5+28x^4+17x^3+67x^2+38x+22$
• $y^2=68x^6+27x^5+50x^4+64x^3+72x^2+9x+15$
• $y^2=10x^6+3x^5+31x^4+57x^3+3x^2+27x+49$
• $y^2=6x^6+15x^5+x^3+71x^2+61x+55$
• $y^2=56x^6+11x^5+58x^4+45x^3+50x^2+52x+51$
• $y^2=51x^6+12x^5+54x^4+16x^3+67x^2+57x+1$
• $y^2=59x^6+68x^5+24x^4+56x^3+51x^2+46x+10$
• $y^2=11x^6+6x^5+12x^4+52x^3+26x^2+22x+43$
• $y^2=45x^6+57x^5+54x^4+28x^3+54x^2+61x+21$
• $y^2=71x^6+7x^5+5x^4+2x^3+2x^2+51x+34$
• $y^2=58x^6+40x^5+15x^4+22x^3+5x^2+40x+60$
• $y^2=4x^6+61x^5+3x^4+29x^3+68x^2+54x+45$
• $y^2=56x^6+33x^5+25x^4+50x^3+71x^2+46x+23$
• $y^2=27x^6+65x^5+40x^4+19x^3+15x^2+47x+21$
• $y^2=64x^6+3x^5+44x^4+41x^3+30x^2+12x+47$
• $y^2=3x^6+64x^5+65x^4+13x^3+34x^2+66x+36$
• $y^2=10x^6+17x^5+38x^4+31x^3+4x^2+64x+2$
• $y^2=62x^6+5x^4+25x^3+39x^2+58x+17$
• $y^2=62x^6+13x^5+60x^4+43x^3+68x^2+48x+9$
• $y^2=19x^6+34x^5+38x^4+4x^3+43x^2+56x+28$

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 3595 27821705 151421457520 806671000390025 4297743609267344875 22902068056173605669120 122044997927822980648792795 650377872685657795124680486025 3465863733993017727240932453179120 18469587794539465474656291712040027625

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 46 5220 389242 28405668 2073128406 151334358510 11047397060662 806460083050308 58871586919641706 4297625834916732100

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{73}$
 The endomorphism algebra of this simple isogeny class is 4.0.109025.1.
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.bc_mz $2$ (not in LMFDB)