Specialize static constexpr data member

I have a class to describe some traits of a type.

template<typename T>
struct my_traits
{
    static constexpr int some_trait = 0;

    static constexpr T min() { return std::numeric_limtis<T>::min(); }
    static constexpr T max() { return std::numeric_limits<T>::max(); }
};

I want to specialize my_traits::some_trait but when I try:

template<> constexpr int my_traits<int>::some_trait = 1;

The compiler complains that my_traits::some_trait already has an initializer. Of course I can specialize it by doing:

template<>
struct my_traits<int>
{
    static constexpr int some_trait = 1;

    // min and max
};

but then I have to redefine all the other functions, even though they will be exactly the same.

So how can I specialize my_traits<int>::some_trait without having to repeat min and max?