We examine the co-jumps of 37 cryptocurrencies based on a network model, and analyse the portfolio implications. The results reveal that, firstly, Bitcoin exerts the strongest influence. Secondly, co-jump heterogeneity exists across pairs of cryptocurrencies with different marketcapitalizations, and the impact of co-jumps is time-varying. Thirdly, the dynamic ranking of co-jump influence shows that, during the COVID-19 pandemic, Bitcoin dominates in the centrality ranking. However, smaller cryptocurrencies (Dogecoin and TRON) exhibit significant co-jump influence. Fourthly, the portfolios constructed based on the co-jump network outperform the baseline strategy by attaining higher returns while experiencing less volatility and shorter downside periods.