585 kWh/m^2 median energy consumption for production according to a 2013 study cited on the Wikipedia article on energy return on investment. 440 W panel has about 2 m^2. It is probably a tad better now, because lower mass of silicon per meter squared. That translates to roughly 2.5 years of energy payback time in Germany under good conditions (azimuth SE to SW and elevation about 30 to 60 degrees, no shadow). Give a few extra months for the inverter and system losses. If you want to know exactly there are commercial databases used for LCA calculations.
The carbon emissions depend on the energy mix of the supply chain (which is mostly in China, since Germany totally butchered domestic production). And the total climate effect is amplified by other emissions (leaking of technical gases in silicon production? But now I am way out of my field of expertise.)
OTOH hand to calculate the offset of emissions you need to know what is going on in the grid. If windmills are shut down around noon to make room for PV, the offset is zero.