Further explorations of Boyd's conjectures and a conductor 21 elliptic curve.

We prove that the (logarithmic) Mahler measure m(P) of P(x, y) = x + 1/x + y + 1/y + 3 is equal to the L-value 2L'(E, 0) attached to the elliptic curve E : P(x, y) = 0 of conductor 21. In order to do this, we investigate the measure of a more general Laurent polynomial Pa,b,c(x, y) = a(x + 1/x)+ b(y + 1/y)+ c and show that the wanted quantity m(P) is related to a 'half-Mahler' measure of Pữ(x, y) = P√7,1,3(x, y). In the finale, we use the modular parametrization of the elliptic curve Pữ(x, y) = 0, again of conductor 21, due to Ramanujan and the Mellit-Brunault formula for the regulator of modular units. [ABSTRACT FROM AUTHOR]