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Goodwill and intangible assets (Tables) | 3 Months Ended | 12 Months Ended
--- | --- | ---
Mar. 31, 2021 | Dec. 31, 2020
Summary of intangible assets | Changes in the carrying amount of intangible assets were as follows:
|  |  |  |  | March 31, 2021 |  |  | December 31, 2020 |
|  | Useful Lives (in years) |  |  | Gross amount |  |  | Accum. amort |  |  | Net amount |  |  | Gross amount |  |  | Accum. amort |  |  | Net amount |
Trademarks |  |  | indefinite |  |  | $ | 50,000 |  |  | $ | — |  |  | $ | 50,000 |  |  | $ | 50,000 |  |  | $ | — |  |  | $ | 50,000 |
Customer relationships |  |  | 4 |  |  |  | 75,000 |  |  |  | (71,875 | ) |  |  | 3,125 |  |  |  | 75,000 |  |  |  | (67,187 | ) |  |  | 7,813 |
Purchased technology |  |  | 5 |  |  |  | 45,423 |  |  |  | (35,314 | ) |  |  | 10,109 |  |  |  | 45,423 |  |  |  | (33,149 | ) |  |  | 12,274 |
Development costs |  |  | 3 |  |  |  | 9,486 |  |  |  | (8,884 | ) |  |  | 602 |  |  |  | 9,486 |  |  |  | (8,434 | ) |  |  | 1,052 |
Software |  |  | 4 |  |  |  | 2,406 |  |  |  | (2,308 | ) |  |  | 98 |  |  |  | 2,406 |  |  |  | (2,181 | ) |  |  | 225 |
Total |  |  |  |  |  | $ | 182,315 |  |  | $ | (118,381 | ) |  | $ | 63,934 |  |  | $ | 182,315 |  |  | $ | (110,951 | ) |  | $ | 71,364 |
| The components of our other intangible assets were as follows (in thousands):
|  |  |  |  | December 31, 2020 |  |  | December 31, 2019 |
|  | Useful Lives |  |  | Gross Amount |  |  | Accum. Amort |  |  | Net Amount |  |  | Gross Amount |  |  | Accum. Amort |  |  | Net Amount |
Trademarks |  |  | indefinite |  |  | $ | 50,000 |  |  | $ | — |  |  | $ | 50,000 |  |  | $ | 50,000 |  |  | $ | — |  |  | $ | 50,000 |
Customer relationships |  |  | 4 years |  |  |  | 75,000 |  |  |  | (67,187 | ) |  |  | 7,813 |  |  |  | 75,000 |  |  |  | (48,437 | ) |  |  | 26,563 |
Purchased technology |  |  | 5 years |  |  |  | 45,423 |  |  |  | (33,149 | ) |  |  | 12,274 |  |  |  | 45,423 |  |  |  | (24,487 | ) |  |  | 20,936 |
Development costs |  |  | 3 years |  |  |  | 9,486 |  |  |  | (8,434 | ) |  |  | 1,052 |  |  |  | 9,486 |  |  |  | (5,096 | ) |  |  | 4,390 |
Software |  |  | 4 years |  |  |  | 2,406 |  |  |  | (2,181 | ) |  |  | 225 |  |  |  | 2,400 |  |  |  | (1,592 | ) |  |  | 808 |
Total |  |  |  |  |  | $ | 182,315 |  |  | $ | (110,951 | ) |  | $ | 71,364 |  |  | $ | 182,309 |  |  | $ | (79,612 | ) |  | $ | 102,697 |
Summary of estimated amortization expense |  | Estimated amortization expense for the years ending December 31, 2021 through 2025 is as follows (in thousands):
Year |  | Expense |
2021 |  | $ | 17,735 |
2022 |  |  | 3,629 |
2023 |  |  | 0 |
2024 |  |  | 0 |
2025 |  |  | 0 |
Summary of amortization expense | The following reflects amortization expense related to intangible assets included with depreciation and amortization:
|  | Three months ended March 31, |
|  | 2021 |  |  | 2020 |
Amortization expense |  | $ | 7.4 million |  |  | $ | 7.9 million |

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