| Rank one quadratic twists of some elliptic curves |
| These tables contain numerical data on the quadratic twists by negative discriminants of the first smallest (for the conductor) elliptic curves. |
The file for each curve consists of a list of vectors (one by line) containing the following data: 1) a fundamental negative discriminant d satisfying additional conditions so that the sign of the functional equation is -1, 2) the short ellinit of the minimal Weierstrass model of the quadratic twist \(E_d\) by d, 3) the product of the Tamagawa numbers of \(E_d\), 4) a generator of the Mordell-Weil group of \(E_d\), 5) the analytic order of the Tate-Shafarevich group of \(E_d\), 6) the index of the subgroup generated by torsion and the Heegner point used in the computation. Note that if the analytic rank of \(E_d\) is greater than 1 then the last three entries are zero.
The lines are ordered by decreasing discriminant and contains all the fundamental discriminants satisfying the additional conditions of absolute value less than \(B\). This file can be imported into PARI/GP using the readvec function.
This is a joint work with C. Delaunay, see Regulators of rank one quadratic twists for more details. All the computations have been done using the PARI/GP system.
|Curve \(11a1\) with \(B = 1 600 000\) (\(222 900\) curves)
|| gp.gz (118Mb)
|Curve \(14a1\) with \(B = 1 600 000\) (\(70 944\) curves)
|| gp.gz (46Mb)
|Curve \(15a1\) with \(B = 1 600 000\) (\(76 004\) curves)
|| gp.gz (53Mb)
|Curve \(17a1\) with \(B = 1 600 000\) (\(229 663\) curves)
|| gp.gz (159Mb)
|Curve \(19a1\) with \(B = 1 600 000\) (\(231 031\) curves)
|| gp.gz (123Mb)