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I've searched everywhere.
No Wikipedia page.
No information on NCBI.
I searched all occurrences of 34/70 in some primary research articles!
The best I've found is this brewery forum where someone asked the same question.

And the user rockfish42 answered:

No idea why they use that number, but it's the catalog number at Weihenstephan's hefebank.

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2 Answers 2

I went to the Yeastbank website at Weihenstephan for some info. The keyword here is "Stamm," which is German for stem, clade, clan, or strain. So, I would take this to mean that the 34/70 is an isolate (#70) of strain 34. Two of 34/70's strengths, according to the link above are it makes clean beer and gives a pleasant taste profile due to its low yeast-like aroma in the finished beer. I can attest to that firsthand, having had on numerous occasions the pleasure of partaking of Weihenstephaner beer in its home city of Freising.

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I am not sure why you say there is no information... a quick Google search returned a few interesting pages...

In this paper:

Progress in Metabolic Engineering of Saccharomyces cerevisiae - Nevoigt, Microbiol Mol Biol Rev. 2008

the author says:

The identification of the entire genomic sequence of a commonly used lager brewer's yeast strain, i.e., Weihenstephan Nr. 34 (34/70), represents a breakthrough in the molecular analysis of lager brewer's yeast.

So, it would look like 34/70 is just a catalogue number, with no specific meaning.

Curiously, according to the Wikipedia page on Saccharomyces pastorianus:

S. pastorianus never grows above 34 °C (93 °F)

So, I cannot exclude the hypothesis that 34 could come from there although, well, I personally propend for the catalogue number.

Other interesting links:

The paper about the S. pastorianus genome sequencing:
Genome sequence of the lager brewing yeast, an interspecies hybrid. - Nakao et al., DNA Res. 2009

An article comparing two different strains of S. pastorianus, 34/70 and 34/78 (again, catalog number hypothesis seems to be the most obvious explanation)

Molecular species of phosphatidylethanolamine from continuous cultures of Saccharomyces pastorianus syn. carlsbergensis strains. - Tosch, Yeast. 2006

The NCBI taxonomy page (entry #520522)

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