Properties

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

Learn more about

Invariants

Base field:  $\F_{463}$
Dimension:  $1$
L-polynomial:  $1 - 42 x + 463 x^{2}$
Frobenius angles:  $\pm0.0699474443693$
Angle rank:  $1$ (numerical)
Number field:  \(\Q(\sqrt{-22}) \)
Galois group:  $C_2$
Jacobians:  2

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 2 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 422 213532 99237098 45953794656 21276729363542 9851127588048604 4561072096072204442 2111776380562936526208 977752464193503818495174 452699390921254827433619932

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 422 213532 99237098 45953794656 21276729363542 9851127588048604 4561072096072204442 2111776380562936526208 977752464193503818495174 452699390921254827433619932

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{463}$
The endomorphism algebra of this simple isogeny class is \(\Q(\sqrt{-22}) \).
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.bq$2$(not in LMFDB)