Properties

Label 1.463.abk
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:  $1 - 36 x + 463 x^{2}$
Frobenius angles:  $\pm0.184580063856$
Angle rank:  $1$ (numerical)
Number field:  \(\Q(\sqrt{-139}) \)
Galois group:  $C_2$
Jacobians:  12

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 12 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 428 214000 99256196 45954360000 21276742514588 9851127824902000 4561072098807333236 2111776380552572640000 977752464191761738334348 452699390921192214751270000

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 428 214000 99256196 45954360000 21276742514588 9851127824902000 4561072098807333236 2111776380552572640000 977752464191761738334348 452699390921192214751270000

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{463}$
The endomorphism algebra of this simple isogeny class is \(\Q(\sqrt{-139}) \).
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.bk$2$(not in LMFDB)