Properties

Label 2.73.aba_lr
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:  $1 - 26 x + 303 x^{2} - 1898 x^{3} + 5329 x^{4}$
Frobenius angles:  $\pm0.0862798287125$, $\pm0.311551167525$
Angle rank:  $2$ (numerical)
Number field:  4.0.606096.2
Galois group:  $D_{4}$
Jacobians:  24

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 24 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 3709 28028913 151475560000 806535138842169 4297551398461044229 22901946625590341760000 122044975700842818524095621 650377904499749674844279135529 3465863766680688229558499353960000 18469587804982121228671381664432243553

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 48 5260 389382 28400884 2073035688 151333556110 11047395048696 806460122499364 58871587474878486 4297625837346598300

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{73}$
The endomorphism algebra of this simple isogeny class is 4.0.606096.2.
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_lr$2$(not in LMFDB)