Properties

Label 1.173.az
Base Field $\F_{173}$
Dimension $1$
Ordinary Yes
$p$-rank $1$
Principally polarizable Yes
Contains a Jacobian Yes

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Invariants

Base field:  $\F_{173}$
Dimension:  $1$
L-polynomial:  $1 - 25 x + 173 x^{2}$
Frobenius angles:  $\pm0.100717649571$
Angle rank:  $1$ (numerical)
Number field:  \(\Q(\sqrt{-67}) \)
Galois group:  $C_2$
Jacobians:  1

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 1 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 149 29651 5175068 895727059 154963900969 26808756665024 4637914408239373 802359179944193475 138808137898917085964 24013807852920796939211

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 149 29651 5175068 895727059 154963900969 26808756665024 4637914408239373 802359179944193475 138808137898917085964 24013807852920796939211

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{173}$
The endomorphism algebra of this simple isogeny class is \(\Q(\sqrt{-67}) \).
All geometric endomorphisms are defined over $\F_{173}$.

Base change

This is a primitive isogeny class.

Twists

Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
1.173.z$2$(not in LMFDB)