Properties

Label 2.73.aba_lp
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:  $1 - 26 x + 301 x^{2} - 1898 x^{3} + 5329 x^{4}$
Frobenius angles:  $\pm0.0641967969525$, $\pm0.317741683996$
Angle rank:  $2$ (numerical)
Number field:  4.0.7579712.2
Galois group:  $D_{4}$
Jacobians:  8

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 8 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 3707 28006385 151414654028 806450157511625 4297473244558291347 22901893795652580191120 122044946446244082497191043 650377887787238539683204415625 3465863754297090609371652779326412 18469587794943208668381299045651209425

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 48 5256 389226 28397892 2072997988 151333207014 11047392400596 806460101776068 58871587264529178 4297625835010677736

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{73}$
The endomorphism algebra of this simple isogeny class is 4.0.7579712.2.
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.ba_lp$2$(not in LMFDB)