The case of the Weierstrass elliptic function with invariants g_2 = - 1 and g_3 = 0. The half-periods for this case are L(1 + i)/4 and L(-1 + i)/4, where L is the lemniscate constant and L/4 = 1.31103... (OEIS A085565).

equianharmonic case | lemniscate case | lemniscate constant | Weierstrass elliptic function