That is a Kyō-yasai[京野菜（きょうやさい）](traditional vegetables from Kyoto) and has cultivated in Kyoto from ancient times. Therefore, that is also called "Kyō-imo[京芋（きょういも）]". But Kyō-imo also refers to Takenoko-imo[タケノコイモ] which is a different taro from Ebi-imo.
In the An-ei[安永（あんえい）] Era(1772-81) of the Edo Period, Shōrenmon-in[青蓮門院（しょうれんもんいん）], who was a royal member and monk, brought that from Nagasaki to Kyoto and the cultivation of Ebi-imo started.
Ebi-imo is harvested from October to February. As it was previously mentioned, Ebi-imo is a Kyō-yasai but Iwata[磐田(いわた)] area in Shizuoka Prefecture has 80% of the share of Ebi-imo now.
Ebi-imo is treated as a luxury foodstuff and that is often used in high-class Japanese-restaurants. That has a fine and sticky texture and that is mildly sweet. That is mainly cooked as boiled dishes with ingredients such as soy sauce and sake. That is used as a dish of Osechi[御節（おせち）] which are dishes eaten in new year's day.
In Kyoto, there is a local dish called "Imo-bō[芋棒（いもぼう）]". Imo-bō is a boiled dish using Ebi-imo and dried cod called "Bō-dara[棒鱈（ぼうだら）]".