# Properties

 Label 2.73.abb_mg 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: $1 - 27 x + 318 x^{2} - 1971 x^{3} + 5329 x^{4}$ Frobenius angles: $\pm0.0678243041225$, $\pm0.294103344880$ Angle rank: $2$ (numerical) Number field: 4.0.4081468.1 Galois group: $D_{4}$ Jacobians: 10

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 10 curves, and hence is principally polarizable:

• $y^2=10x^6+33x^5+63x^4+7x^3+11x^2+9x+35$
• $y^2=6x^6+15x^5+34x^4+22x^3+67x^2+2x+28$
• $y^2=72x^6+60x^5+9x^4+61x^3+43x^2+40x+20$
• $y^2=71x^6+20x^5+4x^4+69x^3+16x^2+34x+9$
• $y^2=31x^6+17x^5+41x^4+61x^3+60x^2+21x+27$
• $y^2=58x^6+46x^5+18x^4+36x^3+16x^2+40x+13$
• $y^2=56x^6+15x^5+2x^4+22x^3+49x^2+11x+45$
• $y^2=25x^6+2x^5+8x^4+15x^3+26x^2+14x+56$
• $y^2=60x^6+42x^5+48x^4+22x^3+25x^2+67x+29$
• $y^2=35x^6+4x^5+12x^4+25x^3+18x^2+25x+19$

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 3650 27907900 151396860800 806518216312000 4297551893233813250 22901927122400295654400 122044936033351003934128850 650377865497401558554118624000 3465863743985487393499327596694400 18469587799113378182734745643655109500

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 47 5237 389180 28400289 2073035927 151333427234 11047391458031 806460074136961 58871587089375020 4297625835981020357

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{73}$
 The endomorphism algebra of this simple isogeny class is 4.0.4081468.1.
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_mg $2$ (not in LMFDB)