Properties

Label 1.433.af
Base Field $\F_{433}$
Dimension $1$
Ordinary Yes
$p$-rank $1$
Principally polarizable Yes
Contains a Jacobian Yes

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Invariants

Base field:  $\F_{433}$
Dimension:  $1$
L-polynomial:  $1 - 5 x + 433 x^{2}$
Frobenius angles:  $\pm0.461664905114$
Angle rank:  $1$ (numerical)
Number field:  \(\Q(\sqrt{-1707}) \)
Galois group:  $C_2$
Jacobians:  10

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 10 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 429 188331 81189108 35151792819 15220865757669 6590636908599744 2853745731211919973 1235671900482318231075 535045932924923274338484 231674888957062523059555611

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 429 188331 81189108 35151792819 15220865757669 6590636908599744 2853745731211919973 1235671900482318231075 535045932924923274338484 231674888957062523059555611

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{433}$
The endomorphism algebra of this simple isogeny class is \(\Q(\sqrt{-1707}) \).
All geometric endomorphisms are defined over $\F_{433}$.

Base change

This is a primitive isogeny class.

Twists

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