• Basic forms
• 栄える — to prosper; to flourish / base form
• 栄えます — prospers; flourishes / masu form
• 栄えた — prospered; flourished / ta form
• 栄えて — flourishing; prospering / te-form
• 栄えない — does not prosper / negative
• 栄えれば — if it prospers / conditional
• 栄えろ・栄えよ — prosper! / imperative
• Other common forms
• 町が栄える — the town prospers
• 文化が栄える — culture flourishes
• More
• 栄えよう — let it flourish / 〜よう form
• 栄えなかった — did not prosper / past negative
• 栄えている — is prospering; is flourishing / progressive

栄える（さかえる） is an ichidan verb. It describes a state of prosperity or flourishing — often used for towns, cultures, businesses, or periods in history rather than individual actions.