# Properties

 Label 2.73.aba_ls 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: $1 - 26 x + 304 x^{2} - 1898 x^{3} + 5329 x^{4}$ Frobenius angles: $\pm0.0960067538857$, $\pm0.308228869049$ Angle rank: $2$ (numerical) Number field: 4.0.9889088.1 Galois group: $D_{4}$ Jacobians: 22

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 22 curves, and hence is principally polarizable:

• $y^2=23x^6+18x^5+25x^4+58x^3+56x^2+62x+30$
• $y^2=14x^6+50x^5+39x^3+59x^2+45x+72$
• $y^2=51x^6+47x^5+4x^4+47x^3+53x^2+6x+58$
• $y^2=34x^6+17x^5+29x^4+28x^3+67x^2+38x+35$
• $y^2=8x^6+21x^5+38x^4+44x^3+32x^2+37x+9$
• $y^2=34x^6+66x^5+51x^4+40x^3+13x^2+32x+1$
• $y^2=29x^6+4x^5+68x^4+36x^3+21x^2+20x+51$
• $y^2=33x^6+50x^5+44x^4+68x^3+69x^2+59x+33$
• $y^2=50x^6+3x^5+22x^4+45x^3+18x^2+20x+22$
• $y^2=30x^6+41x^5+14x^4+50x^3+10x^2+40x+13$
• $y^2=49x^6+30x^5+54x^4+64x^3+35x^2+60x+14$
• $y^2=27x^6+72x^5+18x^4+62x^3+41x^2+27x+47$
• $y^2=5x^6+31x^5+65x^4+43x^3+x^2+70x+14$
• $y^2=21x^6+20x^5+72x^4+42x^3+48x^2+54x+30$
• $y^2=17x^6+12x^5+9x^4+69x^3+5x^2+55x+33$
• $y^2=45x^6+43x^5+59x^4+69x^3+20x^2+18x+65$
• $y^2=33x^6+22x^5+58x^4+60x^3+48x^2+61x+31$
• $y^2=59x^6+63x^5+30x^4+23x^3+61x^2+18x+10$
• $y^2=44x^6+21x^5+4x^4+30x^3+28x^2+29x+60$
• $y^2=34x^6+56x^5+34x^4+6x^3+65x^2+52x+11$
• $y^2=11x^6+54x^5+63x^4+38x^3+22x^2+13x+10$
• $y^2=61x^6+33x^5+31x^4+18x^3+4x^2+40x+20$

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 3710 28040180 151506015710 806577460110800 4297589667109673550 22901971102896752866580 122044987209661020582348110 650377909082734741819431449600 3465863769220620080447450852778830 18469587807040194426047738657665122900

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 48 5262 389460 28402374 2073054148 151333717854 11047396090464 806460128182206 58871587518022080 4297625837825484382

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{73}$
 The endomorphism algebra of this simple isogeny class is 4.0.9889088.1.
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.ba_ls $2$ (not in LMFDB)