Characteristic numbers of families of maps of nodal curves to P2 are defined as intersection of natural divisor classes. (This definition agrees with the usual definition for families of plane curves.) Simple recursions for characteristic numbers of genus one plane curves of all degrees are computed.
"Recursions for characteristic numbers of genus one plane curves." Ark. Mat. 39 (1) 157 - 180, March 2001. https://doi.org/10.1007/BF02388797