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# MA426 - Elliptic Curves

• Module code: MA426
• Module name: Elliptic Curves
• Department: Mathematics Institute
• Credit: 15

## Module content and teaching

###### Principal aims

"This is a sophisticated module making use of a wide palette of tools in pure mathematics. We hope to cover the following topics in varying levels of detail: 1. Non-singular cubics and the group law; Weierstrass equations; 2. Elliptic curves over the rationals; descent, bounding E (Q)/2E (Q), heights and the Mordell-Weil theorem, torsion groups; the Nagell-Lutz theorem; 3. Elliptic curves over complex numbers, elliptic functions; 4. Elliptic curves over finite fields; Hasse estimate, application to public key cryptography; 5. Application to diophantin equations: elliptic diophantine problems, Fermat's Last Theorem; 6. Application to integer factorisation: Pollard's p-1 method and the elliptic curve method. "

###### Departmental link

http://go.warwick.ac.uk/MA426/

###### Other essential notes

Prerequisites:In addition to a general grasp of first and second year algebra and analysis modules, the module involves results from MA246 Number Theory (especially factorisation, modular arithmetic). Knowledge of some parts of MA3B8 Complex Analysis, MA3D5 Galois Theory, MA3A6 Algebraic Number Theory, or MA4A5 Algebraic Geometry may be helpful but not essential.

## Module assessment

Assessment group Assessment name Percentage
15 CATS (Module code: MA426-15)
D (Assessed/examined work) Assessment 15%
3 hour examination (Summer) 85%

## Module availability

This module is available on the following courses:

N/A

N/A

###### Optional
• Undergraduate Mathematics (MMath) (G103) - Year 3
• Undergraduate Mathematics (MMath) (G103) - Year 4
• Undergraduate Master of Mathematics (with Intercalated Year) (G105) - Year 3
• Undergraduate Master of Mathematics (with Intercalated Year) (G105) - Year 4
• Undergraduate Master of Mathematics (with Intercalated Year) (G105) - Year 5
• Undergraduate Mathematics (MMath) with Study in Europe (G106) - Year 3
• Undergraduate Mathematics (MMath) with Study in Europe (G106) - Year 4
• Undergraduate Mathematics and Statistics (BSc MMathStat) (G1G3) - Year 3
• Undergraduate Mathematics and Statistics (BSc MMathStat) (G1G3) - Year 4
• Postgraduate Taught Mathematics (G1P0) - Year 1
• Postgraduate Taught Mathematics (G1P0) - Year 2
• Master of Advanced Study in Mathematical Sciences (G1PE) - Year 1
• Undergraduate Master of Mathematics,Operational Research,Statistics and Economics (G300) - Year 3
• Undergraduate Master of Mathematics,Operational Research,Statistics and Economics (G300) - Year 4
• Undergraduate Master of Mathematics,Operational Research,Statistics and Economics (G30A) - Year 3
• Undergraduate Master of Mathematics,Operational Research,Statistics and Economics (G30A) - Year 4
• Undergraduate Master of Mathematics,Operational Research,Statistics and Economics (G30A) - Year 5
• Undergraduate Master of Mathematics,Operational Research,Statistics and Economics (G30B) - Year 3
• Undergraduate Master of Mathematics,Operational Research,Statistics and Economics (G30B) - Year 4
• Undergraduate Master of Mathematics,Operational Research,Statistics and Economics (G30B) - Year 5
• Undergraduate Master of Mathematics,Operational Research,Statistics and Economics (G30C) - Year 3
• Undergraduate Master of Mathematics,Operational Research,Statistics and Economics (G30C) - Year 4
• Undergraduate Master of Mathematics,Operational Research,Statistics and Economics (G30C) - Year 5
• Undergraduate Master of Mathematics,Operational Research,Statistics and Economics (G30D) - Year 3
• Undergraduate Master of Mathematics,Operational Research,Statistics and Economics (G30D) - Year 4
• Undergraduate Master of Mathematics,Operational Research,Statistics and Economics (G30D) - Year 5
• Undergraduate Master of Mathematics,Operational Research,Statistics and Economics (with Intercalated (G30E) - Year 3
• Undergraduate Master of Mathematics,Operational Research,Statistics and Economics (with Intercalated (G30E) - Year 4
• Undergraduate Master of Mathematics,Operational Research,Statistics and Economics (with Intercalated (G30E) - Year 5
• Undergraduate Master of Mathematics,Operational Research,Statistics and Economics (with Intercalated (G30F) - Year 3
• Undergraduate Master of Mathematics,Operational Research,Statistics and Economics (with Intercalated (G30F) - Year 4
• Undergraduate Master of Mathematics,Operational Research,Statistics and Economics (with Intercalated (G30F) - Year 5
• Undergraduate Master of Mathematics,Operational Research,Statistics and Economics (with Intercalated (G30G) - Year 3
• Undergraduate Master of Mathematics,Operational Research,Statistics and Economics (with Intercalated (G30G) - Year 4
• Undergraduate Master of Mathematics,Operational Research,Statistics and Economics (with Intercalated (G30G) - Year 5
• Undergraduate Master of Mathematics,Operational Research,Statistics and Economics (with Intercalated (G30H) - Year 3
• Undergraduate Master of Mathematics,Operational Research,Statistics and Economics (with Intercalated (G30H) - Year 4
• Undergraduate Master of Mathematics,Operational Research,Statistics and Economics (with Intercalated (G30H) - Year 5
• Undergraduate Discrete Mathematics (G4G3) - Year 4