Properties

Label 1.463.am
Base Field $\F_{463}$
Dimension $1$
Ordinary Yes
$p$-rank $1$
Principally polarizable Yes
Contains a Jacobian Yes

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Invariants

Base field:  $\F_{463}$
Dimension:  $1$
L-polynomial:  $1 - 12 x + 463 x^{2}$
Frobenius angles:  $\pm0.410048877229$
Angle rank:  $1$ (numerical)
Number field:  \(\Q(\sqrt{-427}) \)
Galois group:  $C_2$
Jacobians:  8

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 8 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 452 215152 99267788 45953885376 21276724447892 9851127612907504 4561072100133161372 2111776380604331336448 977752464191607255030884 452699390921189421495534832

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 452 215152 99267788 45953885376 21276724447892 9851127612907504 4561072100133161372 2111776380604331336448 977752464191607255030884 452699390921189421495534832

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{463}$
The endomorphism algebra of this simple isogeny class is \(\Q(\sqrt{-427}) \).
All geometric endomorphisms are defined over $\F_{463}$.

Base change

This is a primitive isogeny class.

Twists

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