The analytic rank of the Mordell elliptic curve y^2=x^3-86069^5 $y^2=x^3-86069^5$ indicates that it has rank 2. However, deriving a set of generators, and hence the regulator, is proving to be a little bit of an intractable problem.

I'm posting this question in the hope that someone may have investigated this curve already and, as such, may be able to help me out with some of the points on the curve.

Any help with this would be very much appreciated.

As further background, I have been involved in a small group searching for values of #Sha > 1 up through the ranks of Mordell curves, currently from ranks 0 to 9.

To date we have been able to progress to a rank 9 curve were #Sha would seem to be at least equal to 9. The details of which may be seen at the NMBRTHRY Archives.

Kevin.

The analytic rank of the Mordell elliptic curve y^2=x^3-86069^5 indicates that it has rank 2. However, deriving a set of generators, and hence the regulator, is proving to be a little bit of an intractable problem.

I'm posting this question in the hope that someone may have investigated this curve already and, as such, may be able to help me out with some of the points on the curve.

Any help with this would be very much appreciated.

As further background, I have been involved in a small group searching for values of #Sha > 1 up through the ranks of Mordell curves, currently from ranks 0 to 9.

To date we have been able to progress to a rank 9 curve were #Sha would seem to be at least equal to 9. The details of which may be seen at the NMBRTHRY Archives.

Kevin.

The analytic rank of the Mordell elliptic curve y^2=x^3-86069^5 indicates that it has rank 2. However, deriving a set of generators, and hence the regulator, is proving to be a little bit of an intractable problem.

I'm posting this question in the hope that someone may have investigated this curve already and, as such, may be able to help me out with some of the points on the curve.

Any help with this would be very much appreciated.

Kevin.