Properties

Label 2.73.abb_mj
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:  $1 - 27 x + 321 x^{2} - 1971 x^{3} + 5329 x^{4}$
Frobenius angles:  $\pm0.103502055686$, $\pm0.282046802349$
Angle rank:  $2$ (numerical)
Number field:  4.0.4390861.1
Galois group:  $D_{4}$
Jacobians:  14

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 14 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 3653 27941797 151491783989 806657800962949 4297688747553314048 22902024861202532182501 122044988449424678021472101 650377887363928122234752945925 3465863752899042348798728577258101 18469587804904770917134385935476477952

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 47 5243 389423 28405203 2073101942 151334073083 11047396202687 806460101251171 58871587240781759 4297625837328599918

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{73}$
The endomorphism algebra of this simple isogeny class is 4.0.4390861.1.
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_mj$2$(not in LMFDB)