Properties

Label 2.73.abc_nb
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:  $1 - 28 x + 339 x^{2} - 2044 x^{3} + 5329 x^{4}$
Frobenius angles:  $\pm0.127660593299$, $\pm0.245090951450$
Angle rank:  $2$ (numerical)
Number field:  4.0.906768.1
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:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 3597 27844377 151487122644 806772362753049 4297848675112538997 22902146252456546254608 122045037383735190830007573 650377880063618638726742798697 3465863724245062705371493548152148 18469587780901782279318854482701115497

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 46 5224 389410 28409236 2073179086 151334875222 11047400632174 806460092198884 58871586754061746 4297625831743425784

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{73}$
The endomorphism algebra of this simple isogeny class is 4.0.906768.1.
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_nb$2$(not in LMFDB)