**Core Concept**
The prophylaxis of migraine involves the use of medications that can reduce the frequency and severity of migraine attacks. This is typically achieved through the modulation of neurotransmitter release, particularly serotonin, which plays a crucial role in the pathophysiology of migraines.

**Why the Correct Answer is Right**
The correct answer, **Propranolol**, is a beta-blocker that has been widely used for the prophylaxis of migraines. It works by inhibiting the release of serotonin from platelets and also has a peripheral vasoconstrictive effect. By reducing the release of serotonin, propranolol can help to decrease the severity and frequency of migraine attacks. Additionally, propranolol's vasoconstrictive effect can help to reduce the dilation of blood vessels that occurs in migraines.

**Why Each Wrong Option is Incorrect**
**Option A:** Sumatriptan is a serotonin receptor agonist used for the acute treatment of migraines, not prophylaxis.
**Option B:** Amitriptyline is a tricyclic antidepressant that can be used for the prophylaxis of migraines, but it is not the most commonly used medication for this purpose.
**Option C:** Ergotamine is a medication used to treat acute migraines, not prophylaxis.

**Clinical Pearl / High-Yield Fact**
When choosing a medication for migraine prophylaxis, it's essential to consider the patient's medical history, including any cardiovascular conditions, as beta-blockers like propranolol can exacerbate these conditions. Regular follow-up and monitoring of the patient's response to treatment are crucial.

**Correct Answer:** C. Ergotamine