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Results tagged with arithmetic-geometry
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user 8441
Diophantine equations, rational points, abelian varieties, Arakelov theory, Iwasawa theory.
17
votes
Accepted
Roadmap to Computer Algebra Systems Usage for Algebraic Geometry
Your question is "Which computer algebra system is best for what, and what is the easiest/most fun(?) way to learn how to deal with them?"
Regarding community, I think Sage (http://sagemath.org) …
17
votes
Accepted
Upper bounds for ranks of modular jacobians
The rank of J0(389) over Q is 13.
The Jacobian splits into factors of dimensions 1,2,3,6,20. Combining explicit computation with Kolyvagin-Gross-zagier implies that the factors of dim 20 has rank 0. …
- 2,368
15
votes
Are there any rational solutions to this equation?
As Dror says, according to Sage it's a genus 2 curve. Homogenizing your equation gives a degree 4 projective plane curve $C$, with arithmetic genus thus $(d-1)(d-2)/2 = 3\cdot 2/2 = 3$. The geometri …
- 2,368