Properties

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

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Invariants

Base field:  $\F_{73}$
Dimension:  $2$
L-polynomial:  $1 - 27 x + 325 x^{2} - 1971 x^{3} + 5329 x^{4}$
Frobenius angles:  $\pm0.146798730614$, $\pm0.260008220746$
Angle rank:  $2$ (numerical)
Number field:  4.0.1516437.3
Galois group:  $D_{4}$
Jacobians:  16

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 16 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 3657 27987021 151618375233 806842334319381 4297863386245838592 22902135548288249443437 122045025189130658400561177 650377874555302381320526594533 3465863723009543013788387172958881 18469587779434819773472078767661756416

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 47 5251 389747 28411699 2073186182 151334804491 11047399528331 806460085368643 58871586733075055 4297625831402083246

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{73}$
The endomorphism algebra of this simple isogeny class is 4.0.1516437.3.
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_mn$2$(not in LMFDB)