Crystal resonator including blank and supporting portion

A crystal resonator, comprising:

• a blank cut out from a crystal parallel to a surface that includes an X″-axis and a Z″-axis, the X″-axis and the Z″-axis being respectively obtained by rotating an X′-axis and a Z′-axis by 45° around a Y′-axis in a direction from the Z′-axis toward the X′-axis, the X′-axis, the Y′-axis, and the Z′-axis being respectively obtained by rotating a crystallographic X-axis, Y-axis, and Z-axis of the crystal by equal to or more than +37° and equal to or less than 51.5° around the X-axis;
• and
• a supporting portion that supports the blank, wherein
• the blank has a reference rectangle having sides respectively parallel to the X″-axis and the Z″-axis, the blank having a shape where at least one pair of opposite sides bulging outward of the reference rectangle, the blank having two longitudinal modes of vibration respectively perpendicular with the X″-axial direction and the Z″-axial direction, and
• the supporting portion is connected to an outer periphery of the blank at a position near an apex of the reference rectangle, the position being where a displacement of vibration in the X″-axial direction or the Z″-axial direction becomes a local minimum when the two longitudinal modes of vibration are coupled.