The L-function $L(s,E)= \sum a_n n^{-s}$ of an Elliptic curve of conductor $N$ has an Euler product of the form \[ L(s,E)=\prod_{p\mid N} \left(1 - a_p p^{-s} \right)^{-1}\prod_{p\nmid N} \left(1 - a_p p^{-s} + p^{-2s} \right)^{-1} \] and satisfies the functional equation \[ \Lambda(s,E)= N^{s/2}\Gamma_{\mathbb C}(s+1/2)\cdot L(s,E)= \varepsilon\Lambda(1-s,E), \] where the sign \(\varepsilon\) is equal to either \(+1\) or \(-1\).

Examples of L-functions attached to isogeny classes of elliptic curves
11.a 14.a 15.a 17.a 19.a 20.a 21.a 24.a 26.a 26.b
27.a 30.a 32.a 33.a 34.a 35.a 36.a 37.a 37.b 38.a
38.b 39.a 40.a 42.a 43.a 44.a 45.a 46.a 48.a 49.a
50.a 50.b 51.a 52.a 53.a 54.a 54.b 55.a 56.a 56.b
57.a 57.b 57.c 58.a 58.b 61.a 62.a 63.a 64.a 65.a