# Properties

 Label 1.463.ax 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: $1 - 23 x + 463 x^{2}$ Frobenius angles: $\pm0.320518658716$ Angle rank: $1$ (numerical) Number field: $$\Q(\sqrt{-3})$$ Galois group: $C_2$ Jacobians: 10

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 10 curves, and hence is principally polarizable:

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 441 214767 99272628 45954339291 21276730636371 9851127444862704 4561072093131188229 2111776380564231123603 977752464194570335260444 452699390921263886380358007

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 441 214767 99272628 45954339291 21276730636371 9851127444862704 4561072093131188229 2111776380564231123603 977752464194570335260444 452699390921263886380358007

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