Properties

Label 2.73.abc_my
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:  $1 - 28 x + 336 x^{2} - 2044 x^{3} + 5329 x^{4}$
Frobenius angles:  $\pm0.0872906235122$, $\pm0.263736764141$
Angle rank:  $2$ (numerical)
Number field:  4.0.1956096.1
Galois group:  $D_{4}$
Jacobians:  12

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 12 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 3594 27810372 151388627994 806620150116624 4297690205981945274 22902026673545928894276 122044974113970976159475562 650377863444059842383567667200 3465863732833251519355593630920586 18469587796005387014008505623669600452

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 46 5218 389158 28403878 2073102646 151334085058 11047394905054 806460071590846 58871586899941774 4297625835257832418

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{73}$
The endomorphism algebra of this simple isogeny class is 4.0.1956096.1.
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_my$2$(not in LMFDB)