Properties

Label 2.73.aba_lt
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:  $1 - 26 x + 305 x^{2} - 1898 x^{3} + 5329 x^{4}$
Frobenius angles:  $\pm0.105254807566$, $\pm0.304726056456$
Angle rank:  $2$ (numerical)
Number field:  4.0.9614400.1
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
$A(\F_{q^r})$ 3711 28051449 151536473244 806619668458041 4297627396894974591 22901994290851156115856 122044996655577123166194591 650377911204335787376995730089 3465863769448671767850589324768476 18469587807334044085315445652102591849

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 48 5264 389538 28403860 2073072348 151333871078 11047396945500 806460130812964 58871587521895794 4297625837893859264

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{73}$
The endomorphism algebra of this simple isogeny class is 4.0.9614400.1.
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.ba_lt$2$(not in LMFDB)