Properties

Label 2.73.abc_mz
Base Field $\F_{73}$
Dimension $2$
Ordinary Yes
$p$-rank $2$
Principally polarizable Yes
Contains a Jacobian Yes

Learn more about

Invariants

Base field:  $\F_{73}$
Dimension:  $2$
L-polynomial:  $1 - 28 x + 337 x^{2} - 2044 x^{3} + 5329 x^{4}$
Frobenius angles:  $\pm0.100935715044$, $\pm0.258299334338$
Angle rank:  $2$ (numerical)
Number field:  4.0.109025.1
Galois group:  $D_{4}$
Jacobians:  20

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 20 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 3595 27821705 151421457520 806671000390025 4297743609267344875 22902068056173605669120 122044997927822980648792795 650377872685657795124680486025 3465863733993017727240932453179120 18469587794539465474656291712040027625

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 46 5220 389242 28405668 2073128406 151334358510 11047397060662 806460083050308 58871586919641706 4297625834916732100

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{73}$
The endomorphism algebra of this simple isogeny class is 4.0.109025.1.
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.
TwistExtension DegreeCommon base change
2.73.bc_mz$2$(not in LMFDB)