Properties

Label 2.73.abc_ne
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:  $( 1 - 14 x + 73 x^{2} )^{2}$
Frobenius angles:  $\pm0.194368965322$, $\pm0.194368965322$
Angle rank:  $1$ (numerical)
Jacobians:  29

This isogeny class is not 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 29 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 3600 27878400 151585635600 806923560960000 4298001922141290000 22902252151718672409600 122045076333007799475171600 650377864081384538585333760000 3465863681233353401239556246787600 18469587737054229210488996280581760000

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 46 5230 389662 28414558 2073253006 151335574990 11047404157822 806460072381118 58871586023459566 4297625821540687150

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{73}$
The isogeny class factors as 1.73.ao 2 and its endomorphism algebra is $\mathrm{M}_{2}($\(\Q(\sqrt{-6}) \)$)$
All geometric endomorphisms are defined over $\F_{73}$.

Base change

This is a primitive isogeny class.

Twists

Below are some of the twists of this isogeny class.
TwistExtension DegreeCommon base change
2.73.a_aby$2$(not in LMFDB)
2.73.bc_ne$2$(not in LMFDB)
2.73.o_et$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.73.a_aby$2$(not in LMFDB)
2.73.bc_ne$2$(not in LMFDB)
2.73.o_et$3$(not in LMFDB)
2.73.a_by$4$(not in LMFDB)
2.73.ao_et$6$(not in LMFDB)