# Properties

 Label 2.73.abb_mj 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: $1 - 27 x + 321 x^{2} - 1971 x^{3} + 5329 x^{4}$ Frobenius angles: $\pm0.103502055686$, $\pm0.282046802349$ Angle rank: $2$ (numerical) Number field: 4.0.4390861.1 Galois group: $D_{4}$ Jacobians: 14

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 14 curves, and hence is principally polarizable:

• $y^2=65x^6+25x^5+52x^4+18x^3+48x^2+50x+45$
• $y^2=44x^6+2x^5+14x^4+71x^3+44x^2+5x+32$
• $y^2=23x^6+2x^5+19x^4+53x^3+32x^2+23x+15$
• $y^2=15x^6+15x^5+40x^4+31x^3+57x^2+11x+61$
• $y^2=59x^6+58x^5+17x^4+43x^3+53x^2+58x+43$
• $y^2=47x^6+46x^5+55x^4+48x^3+52x^2+59x+29$
• $y^2=34x^6+25x^5+41x^4+9x^3+35x^2+12x+30$
• $y^2=19x^6+28x^5+50x^4+64x^3+39x^2+29x+53$
• $y^2=55x^6+54x^5+x^4+56x^3+63x^2+53x+20$
• $y^2=50x^6+67x^5+5x^4+18x^3+21x^2+34x+3$
• $y^2=53x^6+39x^5+12x^4+46x^3+43x^2+25x+21$
• $y^2=28x^6+13x^5+51x^4+34x^3+34x^2+60x+28$
• $y^2=60x^6+5x^5+17x^4+10x^3+72x^2+10x+17$
• $y^2=29x^6+65x^5+19x^4+63x^3+2x^2+35x+40$

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 3653 27941797 151491783989 806657800962949 4297688747553314048 22902024861202532182501 122044988449424678021472101 650377887363928122234752945925 3465863752899042348798728577258101 18469587804904770917134385935476477952

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 47 5243 389423 28405203 2073101942 151334073083 11047396202687 806460101251171 58871587240781759 4297625837328599918

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{73}$
 The endomorphism algebra of this simple isogeny class is 4.0.4390861.1.
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_mj $2$ (not in LMFDB)