Properties

Label 1.73.am
Base Field $\F_{73}$
Dimension $1$
Ordinary Yes
$p$-rank $1$
Principally polarizable Yes
Contains a Jacobian Yes

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Invariants

Base field:  $\F_{73}$
Dimension:  $1$
L-polynomial:  $1 - 12 x + 73 x^{2}$
Frobenius angles:  $\pm0.252180272892$
Angle rank:  $1$ (numerical)
Number field:  \(\Q(\sqrt{-37}) \)
Galois group:  $C_2$
Jacobians:  2

This isogeny class is simple and geometrically simple.

Newton polygon

This isogeny class is ordinary.

$p$-rank:  $1$
Slopes:  $[0, 1]$

Point counts

This isogeny class contains the Jacobians of 2 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 62 5332 389918 28408896 2073133742 151334194324 11047393598702 806460035182848 58871586386922014 4297625829987326932

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 62 5332 389918 28408896 2073133742 151334194324 11047393598702 806460035182848 58871586386922014 4297625829987326932

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{73}$
The endomorphism algebra of this simple isogeny class is \(\Q(\sqrt{-37}) \).
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
1.73.m$2$(not in LMFDB)