How to unit test constructors

I have a class I am adding unit tests to. The class has several constructors which take different types and converts them into a canonical form, which can then be converted into other types.

public class Money {
    public Money(long l) {
        this.value = l;
    }

    public Money(String s) {
        this.value = toLong(s);
    }

    public long getLong() {
        return this.value;
    }

    public String getString() {
        return toString(this.value);
    }
}

In reality there are a couple of other types it accepts and converts to.

I am trying to work out what the most appropriate way to test these constructors is.

Should there be a test per-constructor and output type:

@Test
public void longConstructor_getLong_MatchesValuePassedToConstructor() {
    final long value = 1.00l;

    Money m = new Money(value);
    long result = m.getLong();

    assertEquals(value, result);
}

This leads to a lot of different tests. As you can see, I'm struggling to name them.

Should there be multiple asserts:

@Test
public void longConstructor_outputsMatchValuePassedToConstructor() {
    final long longValue = 1.00l;
    final String stringResult = "1.00";

    Money m = new Money(longValue);

    assertEquals(longValue, m.getLong());
    assertEquals(stringResult, m.getString());
}

This has multiple asserts, which makes me uncomfortable. It is also testing getString (and by proxy toString) but not stating that in the test name. Naming these are even harder.

Am I going about it completely wrong by focussing on the constructors. Should I just test the conversion methods? But then the following test will miss the toLong method.

@Test
public void getString_MatchesValuePassedToConstructor() {
    final long value = 1.00;
    final String expectedResult = "1.00";

    Money m = new Money(value);
    String result = m.getLong();
    assertEquals(expectedResult, result);
}

This is a legacy class and I can't change the original class.