| 1 |
The Projective Plane |
(PDF 1)
(PDF 2) |
| 2 |
Curves in the Projective Plane |
(PDF) |
| 3 |
Rational Points on Conics |
(PDF) |
| 4 |
Geometry of Cubic Curves |
(PDF) |
| 5 |
Weierstrass Normal Form |
(PDF)
(PDF) |
| 6 |
Explicit Formulas for the Group Law |
(PDF) |
| 7 |
Points of Order Two and Three |
(PDF) |
| 8 |
The Discriminant
Points of Finite Order have Integer Coordinates - Part 1 |
(PDF) |
| 9 |
Points of Finite Order have Integer Coordinates - Part 2 |
(PDF) |
| 10 |
Points of Finite Order have Integer Coordinates - Part 3
The Nagell-Lutz Theorem |
(PDF) |
| 11 |
Real and Complex Points on Cubics |
(PDF) |
| 12 |
Heights and Descent |
(PDF) |
| 13 |
Height of P + P_0 |
(PDF) |
| 14 |
Height of 2P |
(PDF) |
| 15 |
A Useful Homomorphism - Part 1 |
(PDF) |
| 16 |
A Useful Homomorphism - Part 2 |
(PDF) |
| 17 |
Mordell's Theorem - Part 1 |
(PDF) |
| 18 |
Mordell's Theorem - Part 2
Examples - Part 1 |
(PDF) |
| 19 |
Examples - Part 2 |
(PDF) |
| 20 |
Examples - Part 3 |
(PDF) |
| 21 |
Singular Cubics |
(PDF) |
| 22 |
Rational Points over Finite Fields |
(PDF) |
| 23 |
Gauss's Theorem - Part 1 |
(PDF) |
| 24 |
Gauss's Theorem - Part 2 |
(PDF) |
| 25 |
Points of Finite Order Revisited |
(PDF) |
| 26 |
Factorization using Elliptic Curves - Part 1 |
(PDF) |
| 27 |
Factorization using Elliptic Curves - Part 2 |
(PDF) |
| 28 |
Integer Points on Cubics
Taxicabs - Part 1 |
(PDF) |
| 29 |
Taxicabs - Part 2
Thue's Theorem - Part 1 |
(PDF) |
| 30 |
Thue's Theorem - Part 2 |
(PDF) |
| 31 |
Construction of an Auxiliary Polynomial |
(PDF) |
| 32 |
The Auxiliary Polynomial is Small |
(PDF) |
| 33 |
The Auxiliary Polynomial Does Not Vanish |
(PDF) |
| 34 |
Proof of the DAT
Further Developments |
(PDF) |
| 35 |
Congruent Numbers and Elliptic Curves I: Koblitz - Part 1 |
(PDF) |
| 36 |
Congruent Numbers and Elliptic Curves II: Koblitz - Part 2 |
(PDF) |