Properties

Label 1.467.ag
Base Field $\F_{467}$
Dimension $1$
Ordinary Yes
$p$-rank $1$
Principally polarizable Yes
Contains a Jacobian Yes

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Invariants

Base field:  $\F_{467}$
Dimension:  $1$
L-polynomial:  $1 - 6 x + 467 x^{2}$
Frobenius angles:  $\pm0.455667945833$
Angle rank:  $1$ (numerical)
Number field:  \(\Q(\sqrt{-458}) \)
Galois group:  $C_2$
Jacobians:  26

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 26 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 462 218988 101855754 47562441696 22211827121022 10372926225657996 4844156487224434842 2262221077790478043008 1056457243345786963318638 493365532643402450697164268

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 462 218988 101855754 47562441696 22211827121022 10372926225657996 4844156487224434842 2262221077790478043008 1056457243345786963318638 493365532643402450697164268

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{467}$
The endomorphism algebra of this simple isogeny class is \(\Q(\sqrt{-458}) \).
All geometric endomorphisms are defined over $\F_{467}$.

Base change

This is a primitive isogeny class.

Twists

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