code: def test_quadratic_elliptical_case():
      # Elliptical case: B**2 - 4AC < 0
  
      assert diop_solve(
          42 * x**2 + 8 * x * y + 15 * y**2 + 23 * x + 17 * y - 4915
      ) == {(-11, -1)}
      assert (
          diop_solve(4 * x**2 + 3 * y**2 + 5 * x - 11 * y + 12)
          == set()
      )
      assert diop_solve(x**2 + y**2 + 2 * x + 2 * y + 2) == {
          (-1, -1)
      }
      assert diop_solve(
          15 * x**2 - 9 * x * y + 14 * y**2 - 23 * x - 14 * y - 4950
      ) == {(-15, 6)}
      assert diop_solve(
          10 * x**2 + 12 * x * y + 12 * y**2 - 34
      ) == {(-1, -1), (-1, 2), (1, -2), (1, 1)}
  
imports: from sympy.core.add import Add
  from sympy.core.mul import Mul
  from sympy.core.numbers import Rational, oo, pi
  from sympy.core.relational import Eq
  from sympy.core.singleton import S
  from sympy.core.symbol import symbols
  from sympy.matrices.dense import Matrix
  from sympy.ntheory.factor_ import factorint
  from sympy.simplify.powsimp import powsimp
  from sympy.core.function import _mexpand
  from sympy.core.sorting import default_sort_key, ordered
  from sympy.functions.elementary.trigonometric import sin
  from sympy.solvers.diophantine import diophantine
  from sympy.solvers.diophantine.diophantine import diop_DN, diop_solve, diop_ternary_quadratic_normal, diop_general_pythagorean, diop_ternary_quadratic, diop_linear, diop_quadratic, diop_general_sum_of_squares, diop_general_sum_of_even_powers, descent, diop_bf_DN, divisible, equivalent, find_DN, ldescent, length, reconstruct, partition, power_representation, prime_as_sum_of_two_squares, square_factor, sum_of_four_squares, sum_of_three_squares, transformation_to_DN, transformation_to_normal, classify_diop, base_solution_linear, cornacchia, sqf_normal, gaussian_reduce, holzer, check_param, parametrize_ternary_quadratic, sum_of_powers, sum_of_squares, _diop_ternary_quadratic_normal, _nint_or_floor, _odd, _even, _remove_gcd, _can_do_sum_of_squares, DiophantineSolutionSet, GeneralPythagorean, BinaryQuadratic
  from sympy.testing.pytest import slow, raises, XFAIL
  from sympy.utilities.iterables import signed_permutations
label_desc: Use image node_id 8 for calling a global function with example usage: test_quadratic_elliptical_case() without return types