IC 418 spans 0.3 light-years across. IC 418 IC 418, also known as Spirograph Nebula, is a planetary nebula in the Milky Way Galaxy. The name derives from the intricate pattern of the nebula, which resembles a pattern which can be created using the Spirograph, a toy that produces geometric patterns (specifically, hypotrochoids and epitrochoids) on paper. Only a few million years ago, IC 418 was probably a common red giant star. Since running out of nuclear fuel, though, the outer envelope has begun expanding outward leaving a hot remnant core destined to become a white dwarf star. IC 418 lies about
Twists of curves its quadratic twist, and only the other two are really new. Also in this case, twisted curves are isomorphic over the field extension given by the twist degree. Analogously to the quartic twist case, an elliptic curve over formula_10 with j-invariant equal to zero can be twisted by cubic characters. The curves obtained are isomorphic to the starting curve over the field extension given by the twist degree. Twists of curves In the mathematical field of algebraic geometry, an elliptic curve E over a field K has an associated quadratic twist, that is another elliptic curve which is isomorphic to