- We have implemented in Magma v2.18-8 the method described in section 5. This methods tries to compute all the rational points of the genus 5 curve attached to a 5-tuple: rationalpoints5tuples.mg (Magma)

OUTPUTs of the examples at section 5.1 using the functions implemented in Magma related to Section 5:

- { 0, 1, 2, 4, 7 }
- { 0, 1, 2, 5, 7 }
- { 0, 1, 3, 7, 8 }
- { 0, 1, 4, 7, 8 } and over Q
- { 0, 3, 5, 6, 10 }
- { 0, 2, 4, 5, 11 }
- { 0, 13, 24, 33, 49 }

- Functions related to subsets of positive integers: Rudin.sage (Sage)

- The following files contain the output related to the computations of all the 5-tuples where our algorithm has finished:

- Resume:

#Positive integers n_{I}associated to equivalences classes of the 5-tuples I of {0,...,51} such thatfile111338all the elliptic quotient of the genus 5 curves C_{I }have only the 8 trivial points424the implementation has obtained all the rational points attached to the corresponding genus 5 curve C_{I}and #C_{I}(Q)>1626165the implementation has obtained all the rational points attached to the corresponding genus 5 curve C_{I}and #C_{I}(Q)=1683716the algorithm does not compute C_{I}(Q) but finishes1033the algorithm does not finish

- For k=5,...,10 the list Tk contains the sorted list of n
_{I}associated to primitive k-tuples I of {0,...,51}such that we have not been able to compute C_{I}(Q)

- For k=5,...,12 the list TBk.sage contains the sorted list of n
_{I}associated to primitive k-tuples I of {0,...,51}such that we have not been able to compute C_{I}(Q) or C_{I}(Q) has more than the 16 trivial points:

- The above lists have been used to prove the Strong and Super-Strong Rudin's Conjectures, and in particular the Table 1 and Table 2:

Last modified: 13/9/2012