Properties

Label 2.73.abb_mf
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:  $1 - 27 x + 317 x^{2} - 1971 x^{3} + 5329 x^{4}$
Frobenius angles:  $\pm0.0527273925472$, $\pm0.297649276576$
Angle rank:  $2$ (numerical)
Number field:  4.0.37525.1
Galois group:  $D_{4}$
Jacobians:  18

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 18 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 3649 27896605 151365223561 806471462409525 4297505155999078144 22901891728632150518845 122044913759025265962756721 650377851978809904244378575525 3465863734487140073251805677362409 18469587791430087843950819621596672000

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 47 5235 389099 28398643 2073013382 151333193355 11047389441779 806460057374083 58871586928034927 4297625834193221550

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{73}$
The endomorphism algebra of this simple isogeny class is 4.0.37525.1.
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.bb_mf$2$(not in LMFDB)