Properties

Label 1.433.ae
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:  $1 - 4 x + 433 x^{2}$
Frobenius angles:  $\pm0.469358705355$
Angle rank:  $1$ (numerical)
Number field:  \(\Q(\sqrt{-429}) \)
Galois group:  $C_2$
Jacobians:  16

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 16 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 430 188340 81187870 35151777600 15220866565150 6590636922839220 2853745730797450030 1235671900471971974400 535045932925101475830670 231674888957069008721915700

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 430 188340 81187870 35151777600 15220866565150 6590636922839220 2853745730797450030 1235671900471971974400 535045932925101475830670 231674888957069008721915700

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{433}$
The endomorphism algebra of this simple isogeny class is \(\Q(\sqrt{-429}) \).
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.e$2$(not in LMFDB)