Share-based compensation - Changes Stock Options (Details) - 12 months ended Dec. 31, 2023	€ / shares shares	$ / shares € / shares shares	$ / shares shares
EUR-denominated \| Euro
Share-based Compensation Arrangement by Share-based Payment Award, Options, Outstanding [Roll Forward]
Number of options, Outstanding, beginning (in shares)	47,607	47,607
Number of options, Granted (in shares)	0	0
Number of options, Exercised (in shares)	(14,768)	(14,768)
Number of options, Forfeited (in shares)	0	0
Number of option, Expired (in shares)	0	0
Number of options, Outstanding, ending (in shares)	32,839	32,839
Number of options, Exercisable (in shares)	32,839	32,839	32,839
Share-based Compensation Arrangement by Share-based Payment Award, Options, Outstanding, Weighted Average Exercise Price [Abstract]
Weighted average exercise price per ordinary share, Outstanding, beginning (in usd/eur per share) \| € / shares	€ 77.95
Weighted average exercise price per ordinary share, Granted (in usd/eur per share) \| € / shares	0
Weighted average exercise price per ordinary share, Exercised (in usd/eur per share) \| € / shares	67.80
Weighted average exercise price per ordinary share, Forfeited (in usd/eur per share) \| € / shares	0
Weighted average exercise price per ordinary share, Expired (in usd/eur per share) \| € / shares	0
Weighted average exercise price per ordinary share, Outstanding, ending (in usd/eur per share) \| € / shares	82.52
Weighted average exercise price per ordinary share (in usd/eur per share) \| € / shares	€ 82.52	€ 82.52
USD-denominated \| US dollar
Share-based Compensation Arrangement by Share-based Payment Award, Options, Outstanding [Roll Forward]
Number of options, Outstanding, beginning (in shares)	32,138	32,138
Number of options, Granted (in shares)	0	0
Number of options, Exercised (in shares)	(8,175)	(8,175)
Number of options, Forfeited (in shares)	0	0
Number of option, Expired (in shares)	(1)	(1)
Number of options, Outstanding, ending (in shares)	23,962	23,962
Number of options, Exercisable (in shares)	23,962	23,962	23,962
Share-based Compensation Arrangement by Share-based Payment Award, Options, Outstanding, Weighted Average Exercise Price [Abstract]
Weighted average exercise price per ordinary share, Outstanding, beginning (in usd/eur per share) \| $ / shares		€ 92.84
Weighted average exercise price per ordinary share, Granted (in usd/eur per share) \| $ / shares		0
Weighted average exercise price per ordinary share, Exercised (in usd/eur per share) \| $ / shares		89.40
Weighted average exercise price per ordinary share, Forfeited (in usd/eur per share) \| $ / shares		0
Weighted average exercise price per ordinary share, Expired (in usd/eur per share) \| $ / shares		92.23
Weighted average exercise price per ordinary share, Outstanding, ending (in usd/eur per share) \| $ / shares		€ 94.01
Weighted average exercise price per ordinary share (in usd/eur per share) \| $ / shares			$ 94.01

The number of shares into which fully or partially vested stock options outstanding as of the balance sheet date can be currently converted under the option plan.

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The weighted-average price as of the balance sheet date at which grantees can acquire the shares reserved for issuance on vested portions of options outstanding and currently exercisable under the stock option plan.

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Number of options or other stock instruments for which the right to exercise has lapsed under the terms of the plan agreements.

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The number of shares under options that were cancelled during the reporting period as a result of occurrence of a terminating event specified in contractual agreements pertaining to the stock option plan.

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Net number of share options (or share units) granted during the period.

+ References

Reference 1: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 718
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 2
-Subparagraph (c)(1)(iv)(01)
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147480429/718-10-50-2

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Number of options outstanding, including both vested and non-vested options.

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Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Topic 718
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
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Reference 2: http://www.xbrl.org/2003/role/disclosureRef
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A roll forward is a reconciliation of a concept from the beginning of a period to the end of a period.

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Weighted average price at which grantees can acquire the shares reserved for issuance under the stock option plan.

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Weighted average price at which option holders acquired shares when converting their stock options into shares.

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Weighted average price at which grantees could have acquired the underlying shares with respect to stock options of the plan that expired.

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Weighted average price at which grantees could have acquired the underlying shares with respect to stock options that were terminated.

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Weighted average per share amount at which grantees can acquire shares of common stock by exercise of options.

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Number of share options (or share units) exercised during the current period.

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Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
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