# Properties

 Label 1.463.abg 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: $1 - 32 x + 463 x^{2}$ Frobenius angles: $\pm0.233124786485$ Angle rank: $1$ (numerical) Number field: $$\Q(\sqrt{-23})$$ Galois group: $C_2$ Jacobians: 18

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 18 curves, and hence is principally polarizable:

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 432 214272 99264528 45954487296 21276741562992 9851127699688704 4561072094491910352 2111776380462068748288 977752464190836699722544 452699390921208354287615232

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 432 214272 99264528 45954487296 21276741562992 9851127699688704 4561072094491910352 2111776380462068748288 977752464190836699722544 452699390921208354287615232

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{463}$
 The endomorphism algebra of this simple isogeny class is $$\Q(\sqrt{-23})$$.
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.bg $2$ (not in LMFDB)