Adolph Göpel had an uncle who was the British consul in Corsica. This enabled Göpel to spend several years in Italy in his youth. He attended mathematics lectures in Pisa during 1825-26 although he was only 13 years old at the time.
In 1829 Göpel entered the University of Berlin where he continued to study after taking his first degree and he was awarded a doctorate in 1835. After this he taught at the Werder Gymnasium and at the Royal Realschule. He then worked as an official in the Royal Berlin Library and had little contact with his mathematical colleagues although he was friends with Crelle for a while.
Göpel's doctoral dissertation studied periodic continued fractions of the roots of integers and derived a representation of the numbers by quadratic forms. He wrote on Steiner's synthetic geometry and an important work, published after his death, continued the work of Jacobi on elliptic functions. This work was published in Crelle's Journal in 1847.
W Burau in [1] writes:-
Göpel started from 16 theta functions in two variables ... and showed that their quotients are quadruply periodic. Of the squares of these 16 functions, four proved to be linearly independent. Göpel linked four more of these quadratics through a homogeneous fourth degree relation, later named the 'Göpel relation' which coincides with the equation of the Kummer surface. Göpel ... finally, after ingenious calculations, obtained the result that the quotients of two theta functions are solutions of the Jacobian problem for p = 2.