Future particle accelerators will require continuous wave operation of SRF cavities capable of supporting high beam currents. An example of this is the Energy Recovery Linac (ERL) at Cornell University, a next generation light source designed to run high currents (100mA) with a high bunch repetition rate (1.3GHz). Obtaining the beam emittance necessary to meet design specification requires strong damping of higher-order modes that can lead to beam breakup. We discuss the optimization and verification of the accelerating cavity. Next we show that an ERL constructed from the optimized cavity geometry – including realistic shape errors – can support beam currents in excess of 300mA while still maintaining beam stability. A niobium prototype 7-cell cavity was fabricated and tested in a horizontal cryomodule. We show that the prototype cavity exceeds quality factor and gradient specifications of 2×1010 at 16.2MV/m at 1.8K by 50%, reaching Q=(3.0±0.3)×1010. The prototype cavity also satisfies all design constraints and has a higher order mode spectrum consistent with the optimized shape geometry. At 1.6K, the cavity set a record for quality factor of a multicell cavity installed in a horizontal cryomodule reaching Q=(6.1±0.6)×1010.