No, eternal life is a free gift because God is a loving and good God of ‘grace’, and the faith to believe is a free gift through His Holy Spirit to you;
“For by grace you have been saved through faith. And this is not your own doing; it is the gift of God, not a result of works, so that no one may boast. For we are his workmanship, created in Christ Jesus for good works, which God prepared beforehand, that we should walk in them.”
Ephesians 2:8-10
Only God will receive the glory for our being saved. And belief in this results in our good works empowered by the Spirit of God as we live new lives obedient to Him.