History of Regulators of elliptic curves over $\mathbb{Q}$ of rank $1$

 Parameters:   N:-    title: conductor of $E$+    title: conductor     type: Z   c4:     display: $c_4$-    title: invariant $c_4$ of a minimal model of $E$+    title: $c_4$ invariant of a minimal model     type: Z   c6:     display: $c_6$-    title: invariant $c_6$ of a minimal model of $E$+    title: $c_6$ invariant of a minimal model     type: Z Comments:   comment-redundancy-of-N: The conductor $N$ can be deduced from $c_4$ and $c_6$.     We display it for convenience.-  comment-E-from-c4c6: 'A model of $E/\mathbb{Q}$ is given by $E: y^2 = x^3 - 27 c_4-    x - 54 c_6$.' Formulas:   formula-height-pairing-matrix: For an elliptic curve $E$ over a number field $K$,  $\text{Reg}(E/K)