# Properties

 Label 2.73.abb_ml 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: $1 - 27 x + 323 x^{2} - 1971 x^{3} + 5329 x^{4}$ Frobenius angles: $\pm0.124803810750$, $\pm0.272272309487$ Angle rank: $2$ (numerical) Number field: 4.0.3128013.1 Galois group: $D_{4}$ Jacobians: 18

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 18 curves, and hence is principally polarizable:

• $y^2=53x^6+3x^5+60x^4+56x^3+23x^2+59x+72$
• $y^2=5x^6+58x^5+35x^4+49x^3+70x^2+55x$
• $y^2=52x^6+20x^5+17x^4+53x^3+36x^2+16x+22$
• $y^2=x^6+27x^5+65x^4+8x^3+46x^2+3x+26$
• $y^2=7x^6+58x^5+43x^4+25x^3+9x^2+51x+43$
• $y^2=49x^5+2x^4+67x^3+48x^2+11x+37$
• $y^2=60x^6+64x^5+30x^4+63x^3+48x^2+8x+14$
• $y^2=55x^6+37x^5+44x^4+39x^3+17x^2+12x+45$
• $y^2=20x^6+38x^5+7x^4+4x^3+64x^2+9x+37$
• $y^2=31x^6+55x^5+27x^4+47x^3+66x^2+9x+23$
• $y^2=40x^6+32x^5+52x^4+58x^3+68x^2+62x+13$
• $y^2=29x^6+46x^5+14x^4+25x^3+41x^2+47x+62$
• $y^2=5x^6+53x^5+60x^4+16x^3+65x^2+41x+59$
• $y^2=51x^6+19x^5+17x^4+3x^3+45x^2+57x+34$
• $y^2=12x^6+39x^5+29x^4+23x^3+41x^2+65x+65$
• $y^2=2x^6+50x^5+70x^4+39x^3+15x^2+58x+29$
• $y^2=6x^6+42x^5+37x^4+34x^3+7x^2+25x+20$
• $y^2=47x^6+2x^5+29x^4+11x^2+70x+13$

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 3655 27964405 151555075735 806750293259925 4297777185989508400 22902083003160702277405 122045011513001851447160695 650377886807856942720105502725 3465863743574124172417534602468655 18469587796287264700614835135758726400

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 47 5247 389585 28408459 2073144602 151334457279 11047398290381 806460100561651 58871587082387555 4297625835323421582

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{73}$
 The endomorphism algebra of this simple isogeny class is 4.0.3128013.1.
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.bb_ml $2$ (not in LMFDB)