# Properties

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

## Invariants

 Base field: $\F_{463}$ Dimension: $1$ L-polynomial: $1 - 43 x + 463 x^{2}$ Frobenius angles: $\pm0.0128146746178$ Angle rank: $1$ (numerical) Number field: $$\Q(\sqrt{-3})$$ Galois group: $C_2$ Jacobians: 1

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 1 curves, and hence is principally polarizable:

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 421 213447 99233068 45953644971 21276724519471 9851127444862704 4561072092108458809 2111776380458651435763 977752464190871876438404 452699390921190720634700607

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 421 213447 99233068 45953644971 21276724519471 9851127444862704 4561072092108458809 2111776380458651435763 977752464190871876438404 452699390921190720634700607

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{463}$
 The endomorphism algebra of this simple isogeny class is $$\Q(\sqrt{-3})$$.
All geometric endomorphisms are defined over $\F_{463}$.

## Base change

This is a primitive isogeny class.

## Twists

Below are some of the twists of this isogeny class.
 Twist Extension Degree Common base change 1.463.br $2$ (not in LMFDB) 1.463.u $3$ (not in LMFDB) 1.463.x $3$ (not in LMFDB)
Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 1.463.br $2$ (not in LMFDB) 1.463.u $3$ (not in LMFDB) 1.463.x $3$ (not in LMFDB) 1.463.ax $6$ (not in LMFDB) 1.463.au $6$ (not in LMFDB)