This page has links to all the data concerning

The data concerns polynomials of the form

After discarding preperiodic points, the question is:
how small can the canonical height of *z*
(for the map *z*^{2} - *c*)
be, relative to the (standard) height of *c*?

The following two comma-separated text files list all
such pairs (*c*,*z*) where the ratio of the
two heights is less than about 0.037:

*n* not divisible by 4
*n* divisible by 4

**Reading the data files:**

Each line of each data file is in the format

`
c,z,[canonical height h_c(z) of z],[height ratio h_c(z)/h(c)]
`

Here is a sample entry, which appears in the
``*n* divisible by 4'' file:

`
1013082841/476985600,10541/21840,0.3076249143,0.0148351177
`

This means the point 10541/21840 has canonical height
about 0.30762 for the map
*z*^{2} - 1013082841/476985600.
Dividing this height by *h*(1013082841/476985600)=
log(1013082841) gives the height ratio of about
0.014835.