Chapter 32- The q Octic Transform

Equating the octahedral form and the elliptic modular form of the j-invariant resulted in equations between different quadratic field q-octic continued fractions.  These q-octic forms are transformed through radical expressions defined by the R and C transform.  Interesting properties are shown for these transforms using integer and fractional arguments.   The transforms are modular-like in complex multiplication and can be applied to the proper calculation of the j-invariant for various class equations from the q-octic continued fraction.

(updated 6/15/2019)

The q-Octic Transforms