Properties

 Label 2.73.abe_of 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: $1 - 30 x + 369 x^{2} - 2190 x^{3} + 5329 x^{4}$ Frobenius angles: $\pm0.0896851289724$, $\pm0.207445605396$ Angle rank: $2$ (numerical) Number field: 4.0.155200.2 Galois group: $D_{4}$ Jacobians: 6

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 6 curves, and hence is principally polarizable:

• $y^2=33x^6+13x^5+41x^4+28x^3+49x^2+46x+42$
• $y^2=61x^6+52x^5+32x^4+12x^3+38x^2+46x+68$
• $y^2=7x^6+51x^5+67x^4+68x^3+50x^2+58x+68$
• $y^2=40x^6+42x^5+60x^4+65x^3+9x^2+4x+21$
• $y^2=45x^6+x^5+20x^4+59x^3+6x^2+36x+63$
• $y^2=43x^6+28x^5+43x^4+71x^3+43x^2+19x+30$

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 3479 27550201 151194570716 806590568251321 4297782867694392839 22902146748843298512016 122045053743127283027228711 650377886722839255284870502825 3465863718922499496911830353943964 18469587771693039120756317641676530921

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 44 5168 388658 28402836 2073147344 151334878502 11047402113008 806460100456228 58871586663652034 4297625829600674528

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{73}$
 The endomorphism algebra of this simple isogeny class is 4.0.155200.2.
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.be_of $2$ (not in LMFDB)