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The function supersingular_j returns one such supersingular j-invariant :

sage: supersingular_j(GF(19^2, 'a'))
18
sage: supersingular_j(GF(15073^2, 'a'))
4443*a + 13964

The function supersingular_j returns one such supersingular j-invariant :

sage: supersingular_j(GF(19^2, 'a'))
'i'))
18
sage: supersingular_j(GF(15073^2, 'a'))
4443*a 'i'))
4443*i + 13964

The function supersingular_j returns one such supersingular j-invariant :

sage: supersingular_j(GF(19^2, 'i'))
18
sage: supersingular_j(GF(15073^2, 'i'))
4443*i + 13964

To get all of them you use the method supersingular_points:

sage: S = SupersingularModule(19)
sage: S
Module of supersingular points on X_0(1)/F_19 over Integer Ring
sage: L,d = S.supersingular_points()
sage: L
[18, 7]
sage: S = SupersingularModule(431)
sage: L,d = S.supersingular_points()
sage: len(L)
37