# 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:

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

 $r$ 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.
 Twist Extension Degree Common base change 1.463.bk $2$ (not in LMFDB)