(no they are not born in an egg, this is just artful photography)
Reproduction
Females (cows) reach sexual maturity at around 9-12 years of age and become pregnant for the first time, on average, around age 13.
They can reproduce until ages 55-60. Females give birth at intervals of about every 5 years. An elephant's gestation (pregnancy) period lasts about 22 months (630-660 days), the longest gestation period of any mammal, after which typically one calf is born. Twins are rare.
Labor ranges in length from 5 minutes to 60 hours. The average length of labor is 11 hours.
At birth, calves weigh around 90–115 kg (200–250 lb), and they gain 1 kg (2–2.5 lb) a day. In the wild, the mother is accompanied by other adult females (aunts) that protect the young, and baby elephants are raised and nurtured by the whole family group, practically from the moment they are born.