# Properties

 Label 2.73.abb_mn 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: $1 - 27 x + 325 x^{2} - 1971 x^{3} + 5329 x^{4}$ Frobenius angles: $\pm0.146798730614$, $\pm0.260008220746$ Angle rank: $2$ (numerical) Number field: 4.0.1516437.3 Galois group: $D_{4}$ Jacobians: 16

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 16 curves, and hence is principally polarizable:

• $y^2=52x^6+48x^5+38x^4+10x^3+35x^2+40x+21$
• $y^2=30x^6+47x^4+25x^3+43x^2+22x+8$
• $y^2=37x^6+8x^5+65x^4+12x^3+26x^2+30x+28$
• $y^2=52x^6+12x^5+22x^4+38x^3+40x^2+14x+48$
• $y^2=42x^6+59x^5+41x^3+21x^2+28x+34$
• $y^2=62x^6+31x^5+71x^4+66x^3+11x^2+66x+19$
• $y^2=33x^6+38x^5+62x^4+63x^3+10x^2+43x+34$
• $y^2=55x^6+8x^5+40x^4+4x^3+63x^2+49x+56$
• $y^2=41x^6+29x^5+40x^4+44x^3+21x^2+42x+53$
• $y^2=39x^6+67x^5+51x^4+32x^3+16x^2+50x+24$
• $y^2=2x^6+41x^5+26x^4+40x^3+64x^2+67x+42$
• $y^2=62x^6+20x^4+40x^3+19x^2+68x$
• $y^2=59x^6+35x^5+26x^4+70x^3+38x^2+70x+57$
• $y^2=56x^6+35x^5+8x^4+8x^3+23x^2+16x+34$
• $y^2=36x^6+7x^5+55x^4+47x^3+5x^2+50x+9$
• $y^2=15x^6+43x^5+58x^4+60x^3+36x^2+37x+9$

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 3657 27987021 151618375233 806842334319381 4297863386245838592 22902135548288249443437 122045025189130658400561177 650377874555302381320526594533 3465863723009543013788387172958881 18469587779434819773472078767661756416

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 47 5251 389747 28411699 2073186182 151334804491 11047399528331 806460085368643 58871586733075055 4297625831402083246

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{73}$
 The endomorphism algebra of this simple isogeny class is 4.0.1516437.3.
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_mn $2$ (not in LMFDB)