Properties

Label 2.73.abc_mw
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:  $1 - 28 x + 334 x^{2} - 2044 x^{3} + 5329 x^{4}$
Frobenius angles:  $\pm0.0555528882213$, $\pm0.273187710002$
Angle rank:  $2$ (numerical)
Number field:  4.0.23552.1
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
$A(\F_{q^r})$ 3592 27787712 151322974984 806518111345664 4297581658660955272 22901939330228900040128 122044918249514064774569608 650377833617271068127351652352 3465863717849690520307947445994248 18469587787090132050632175902064487872

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 46 5214 388990 28400286 2073050286 151333507902 11047389848254 806460034606014 58871586645429166 4297625833183371934

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{73}$
The endomorphism algebra of this simple isogeny class is 4.0.23552.1.
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.bc_mw$2$(not in LMFDB)