Celtic's reputation for putting pounds in the bank only increased when they published their latest stellar financial figures on Monday. Now that the Champions League is upon them, it's time to put points on the board.

For a decade and more, Celtic's Champions League group-stage story usually began against a giant - Real Madrid in 2022, Paris St-Germain in 2017, Barcelona in 2016, Milan in 2013 and, in 2012, Benfica - not a behemoth but good enough to be Europa League finalists some months later.

They lost four and drew one of those. In 12 attempts, Celtic have never won their first game in the group phase. The format has changed though and perhaps their fate is about to change with it.

In Slovan Bratislava they are playing a collection of free transfers, academy graduates and six-figure signings. Celtic's squad has been assembled for close to £70m, about £67m more than their opponents on Wednesday night at Celtic Park have spent.

Eleven different Celtic players were bought for a higher fee than the fees of all of Slovan's players put together. All those usual arguments about Celtic competing against the financial might of Europe's heavyweights do not apply. They have not had a more winnable game at this stage of the competition since hosting Aalborg in 2008.

That is a cautionary tale, of course. Celtic were hot favourites. They earned a penalty and missed it. They played the closing stages against 10 men but could not take advantage. It ended 0-0.

Those at Celtic who know their recent European history will not be counting their chickens but the Champions League draw, and the schedule of fixtures, have given Brendan Rodgers' side a glorious opportunity to begin this tournament with a bang for a change.

It is a chance they dare not miss. In their own place, Celtic should be too good for Slovan.

The form of Rodgers' team is encouraging. They are playing at a higher tempo than last season, their pressing game, work-rate and creativity look good. They have signed well. They have a bit of a strut about them.

The caveat is we are judging them on domestic form, a barometer that has blown up in everybody's face in the past.

Are Celtic more than mere flat-track bullies? We are about to get some answers in Europe. This is their testing ground, not Scotland where they are odds-on to skate away with the Premiership. The Champions League will show Celtic's worth and indeed, Rodgers' worth.

With his domestic dominance he has written his name into the fabric of the club but Rodgers' record with Celtic in Europe is poor. He's been manager in 18 Champions League group games, winning two, losing 12 and drawing four.

His team has scored 15 goals with 49 conceded. In among that lot, there are 5-0, 6-0, 7-0 and 7-1 defeats. The strange paradox is that many of the worst European results in Celtic's history have come under one of their most convincing leaders.

When you include Europa League games, Rodgers' European record at Celtic is six won, 18 lost and four drawn (of the 28 played). Rodgers has mentioned his desire to improve on that. Deep down you sense it is not just a wish but a raging ambition to make Celtic relevant in Europe again.

Until they do something about it, their failures will be thrown in their face. There were many matches nobody expected Celtic to win but there are others they could have won but did not, for various reasons.

These are the lessons they must learn for this campaign. Discipline, concentration, ruthlessness. Discover their inner dog. A rottweiler rather than a poodle.

Last season, they were shown two red cards away to Feyenoord in their opening game and lost 2-0. Against Lazio at home they lost in the 90th minute. They were in front twice against Atletico Madrid but drew 2-2. They conceded three times in 16 minutes in Madrid and twice in three minutes in Rome.

That propensity to concede and then concede again quickly has derailed Rodgers' teams. In the Europa League in the last season of his first spell in 2018-19, they conceded two in six minutes against Salzburg, two in four minutes against Leipzig and two in seven minutes against Valencia.

In other Champions League games, they conceded two in two minutes and another two in six minutes on the same night against PSG. Yes, it was PSG but serious resilience was required and Rodgers' team didn’t have it.

In the return game they lost two in four minutes and another two in six minutes. They shipped three goals in 10 minutes against Barcelona in 2016 and led three times against Manchester City, only to get pegged back each time. A 3-3 draw was a really good result but it might have been more.

In his one Champions League season, Ange Postecoglou had a similar issue with his side conceding goals in clusters. These are snapshots from the past but last season's missed opportunities showed they were still relevant.

It is in Rodgers' DNA to send his team out with an attacking mindset but a hardened pragmatism has to be part of the make-up now as well. Offensive, yes, but bloody-minded and obdurate too. On a stage as unforgiving as Europe, there's nothing wrong with grinding it out and winning ugly.

Wednesday night ought to see a Celtic win - ugly or otherwise, it does not really matter. But what else can they achieve in the months ahead? They have good individuals but if they are to finish in a comfortable play-off place - which is wholly achievable - it is collective steel they need now.