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Rob Moffat's men have lost all three fixtures to date yet they have a points difference of just minus 10.
A 18-17 reverse at Cardiff Blues on the opening weekend of European action was followed by a heartbreaking 37-21 defeat at home to pool leaders Northampton Saints in an absolute thriller before last weekend's 21-16 loss in France.
And despite winning plenty of plaudits for the manner of their continental performances, Moffat insists Sunday's rematch with Castres is simply about winning.
"We haven't been far away in any of our European matches to date, but our ambitions are much higher than picking up losing bonus points," said Moffat.
"We've got a good record at home in the Heineken Cup over the last couple of years, and we really want to add another win to that sequence.
"It's vital for us and the support that we prove we can win at this level and give ourselves a boost ahead of a massive couple of weeks.
"Sunday's game is all about getting a win in the Heineken Cup and getting some momentum to take into the Glasgow matches (in the Magners League)."
A repeat of the bonus-point triumph over the same opposition at Murrayfield two seasons ago would do nicely for Edinburgh.
That 32-14 win was the first of four straight home successes in the Heineken Cup prior to October's defeat to Northampton and Moffat would gladly accept a similar outcome this time around.
"We played really well that day and showed a lot of ambition in attack," added Moffat.
"If we perform to the same level, giving ourselves the right platform to build, I've every confidence we'll get the result that everyone is looking for on Sunday."
