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Share-based compensation - Stock Options (Details) € / shares in Units, $ / shares in Units, € in Millions, $ in Millions | 12 Months Ended |  |  |
--- | --- | --- | --- | ---
Dec. 31, 2025 EUR (€) € / shares | Dec. 31, 2025 USD ($) $ / shares | Dec. 31, 2024 EUR (€) € / shares | Dec. 31, 2024 USD ($) $ / shares | Dec. 31, 2023 EUR (€) € / shares | Dec. 31, 2023 USD ($) $ / shares | Dec. 31, 2025 USD ($) | Dec. 31, 2024 USD ($) | Dec. 31, 2023 USD ($)
EUR-denominated |  |  |  |  |  |  |  |  |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |  |  |  |  |  |  |
Weighted average share price at stock option exercise (in usd/eur per share) | € / shares | € 722.84 |  | € 834.48 |  | € 613.03 |  |  |  |
Aggregate intrinsic value of exercised stock options (in millions) | € | € 8.8 |  | € 10.2 |  | € 8.1 |  |  |  |
Weighted average remaining contractual term of exercisable options (in years) | 3 months 25 days | 3 months 25 days | 9 months 29 days | 9 months 29 days | 1 year 5 months 23 days | 1 year 5 months 23 days |  |  |
Aggregate intrinsic value of exercisable stock options (in millions) | € | € 4.6 |  | € 11.4 |  | € 19.7 |  |  |  |
Aggregate intrinsic value of outstanding stock options (in millions) | € | € 4.6 |  | € 11.4 |  | € 19.7 |  |  |  |
USD-denominated |  |  |  |  |  |  |  |  |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |  |  |  |  |  |  |
Weighted average share price at stock option exercise (in usd/eur per share) | $ / shares |  | $ 840.14 |  | $ 911.23 |  | $ 678.41 |  |  |
Aggregate intrinsic value of exercised stock options (in millions) | $ |  | $ 6.8 |  | $ 8.2 |  | $ 4.8 |  |  |
Weighted average remaining contractual term of exercisable options (in years) | 3 months 18 days | 3 months 18 days | 10 months 2 days | 10 months 2 days | 1 year 5 months 4 days | 1 year 5 months 4 days |  |  |
Aggregate intrinsic value of exercisable stock options (in millions) | $ |  |  |  |  |  |  | $ 4.5 | $ 8.2 | $ 15.9
Aggregate intrinsic value of outstanding stock options (in millions) | $ |  |  |  |  |  |  | $ 4.5 | $ 8.2 | $ 15.9

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- Definition Line items represent financial concepts included in a table. 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- Definition Amount of accumulated difference between fair value of underlying shares on dates of exercise and exercise price on options exercised (or share units converted) into shares. + References Reference 1: http://www.xbrl.org/2003/role/disclosureRef -Topic 718 -SubTopic 10 -Name Accounting Standards Codification -Section 50 -Paragraph 2 -Subparagraph (d)(2) -Publisher FASB -URI https://asc.fasb.org/1943274/2147480429/718-10-50-2 + Details
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