How should I update existing table in the SQL Server database via C# and Windows forms?

I want to use Windows Forms and C# to implement a Database application which consists of the following tables:

Student table:

CREATE TABLE [dbo].[Student] 
(
    [Id]   INT          NOT NULL,
    [Name] NVARCHAR(50) NOT NULL,
    [MyId] AS ('S' + RIGHT('00' + CONVERT([varchar](5), [Id]), (2))) PERSISTED,
    PRIMARY KEY CLUSTERED ([Id] ASC)
);

Class table:

CREATE TABLE [dbo].[Class] 
(
    [Id]      INT          NOT NULL,
    [Teacher] NVARCHAR(50) NOT NULL,
    [Grade]   INT          NOT NULL,
    PRIMARY KEY CLUSTERED ([Id] ASC)
);

StudentClassCombo:

CREATE TABLE [dbo].[StudentClassCombo]  
(
    [ClassID]   INT NOT NULL,
    [StudentID] INT NOT NULL,
    CONSTRAINT [ClassFK] 
        FOREIGN KEY ([ClassID]) REFERENCES [dbo].[Class] ([Id]),
    CONSTRAINT [StudentFK] 
        FOREIGN KEY ([StudentID]) REFERENCES [dbo].[Student] ([Id])
);

I have a Windows forms interface through which I can assign students to classes.

I want to ensure that when the a student that has already been assigned to a class is re-assigned to a different class. the previous student-class assignment should be overwritten with the new one. In the case above, if Student ID 1 is already assigned to Class ID 1. But if the user decides to re-assign Student ID 1 to Class ID 2, the existing StudentClassCombo entry of 1-1 should be changed to 1-2.

I have written the following code to perform this update but I am encountering an exception:

string UpdateQuery = @"UPDATE dbo.StudentClassCombo SET"
                      + " Class.ID as ClassId, Student.Id as StudentId FROM dbo.Class, dbo.Student" +
                      " WHERE Class.Grade=@Grade and Student.Name LIKE @StudentName";


using (connection = new SqlConnection(connectionString))
using (SqlCommand Insertcmd = new SqlCommand(UpdateQuery, connection))
{
    connection.Open();

    Insertcmd.Parameters.Add("@Grade", SqlDbType.Int);
    Insertcmd.Parameters.Add("@StudentName", SqlDbType.NVarChar, 50);

    foreach (ListViewItem eachItem in StudentsList.CheckedItems)
    {
        Insertcmd.Parameters["@Grade"].Value = int.Parse(ClassNames.Text);
        Insertcmd.Parameters["@StudentName"].Value = eachItem.SubItems[1].Text.ToString();
                    
        Insertcmd.ExecuteNonQuery();
    }

    connection.Close();
}

The exception I am seeing now is as follows:

An unhandled exception of type 'System.Data.SqlClient.SqlException' occurred in System.Data.dll

Additional information: Incorrect syntax near the keyword 'as'.

How should I update the StudentClassCombo entries?