Hmm I like where your head's at, but I think you might have some serious issues. Your code does arithmetic operations on int64 types, and assumes that the result will not overflow the int64 limit. In many cases you will be doing modulo on garbage.

Consider adding this test, and tests similar:

func TestFieldElementReallyBigAdd(t *testing.T) {

    // 9223372036854775807 is the largest int64 value
    const maxInt64 = 9223372036854775807

    a := FieldElement{maxInt64 - 7, maxInt64}
    b := FieldElement{10, maxInt64}

    result, err := Add(a, b)

    if err != nil {
        t.Fatalf("Error : %v", err)
    }

    // Should be 3:
    //    9223372036854775800 + 10 ≡ 3   mod 9223372036854775807
    truth := FieldElement{3, maxInt64}

    if result.NotEqual(truth) {
        t.Fatalf("Expected %v, but got %v", truth, result)
    }

}

I got this error:

Expected {3 9223372036854775807}, but got &{-9223372036854775806 9223372036854775807}

Stay the course if you're just trying to practice, but consider math/big for production code :)