Jazz Chords are built using the characteristic notes of each mode of every scale. The chord types can be quite complex (like dom7alt) but the basic alterations for the major scale, in relation to the tonic, are as follows:
I:(Ionian or major) no alterations, since all alterations are based of the tonic major chord with its regular 1st, 3rd, 5th, and 7th
ii:(dorian) the same as the natural minor mode (b3,b6,b7) except for the sixth, which is not flatted
iii: (phrygian) the same as the natural minor mode except for its for b2
IV: (Lydian) contains a #4
V: (Mixolydian)
vi:(natural minor mode, or aeolian) b3,b6,b7
vii: (diminished mode, or locrian) same as phrygian, with the addition of the b5, or diminished fifth
One possible cause of your misunderstanding might be the '#11'. a sharped 11th is the same as a sharped fourth, only it is up an octave. Chord notation, when describing alterations, uses the original degree within the seven-note scale. When a specially labeled note, like the sharped fourth in your case, is one or more octaves higher then the bass note, the number is increased by seven to indicate the higher octave. So basically, a sharped fourth is the same as a sharped 11th, except the sharped 11th is an octave higher.
1 3 5 7
. This chord you are asking about is usually has1 3 4 7
. Fun fact - the tune Lost Woods from Zelda The Ocarina of Time is entirely built on the Lydian mode. Cool stuff