46

Answers

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3

Can one bound the Quadratic Points on Curves?

4

Field of definition of canonical morphism between (congruence) modular curves

3

ramified quaternion algebras

8

Deducing BSD from Gross-Zagier and Kolyvagin

1

Fuchsian groups and automorphisms of Riemann surfaces

2

the dual abelian scheme

1

How do you find the genus of a Fuchsian group derived from a quaternion algebra?

7

Supersingular Elliptic Curves with rational isogeny?

6

How does a moduli interpretation give an analytic object an algebraic structure?

2

Imaginary quadratic field contained in Hecke orbit field?

9

The significance of modularity for all Galois representations

7

Intersection of Hilbert class fields of imaginary quadratic fields

12

Isogeny classes of elliptic curves

3

elliptic curves with and without CM

4

Volumes of fundamental domains of maximal orders in definite quaternion algebras over Q

4

Uniform bounds for the order of a rational torsion point on CM elliptic curves

6

Is the number of twists of a curve with a section in a given field finite

2

Open problems with monetary rewards

8

Stacks in modern number theory/arithmetic geometry

8

Average rank of elliptic curves over $\mathbb{Q}$

3

‘Reference’ request: Program to work with cyclic quotient singularities.

2

Applications for knowing the singularities parametrized by the boundary of a moduli space

1

Curves which are not covers of P^1 with four branch points

7

Atkin-Lehner involution and class number

4

What is the high-concept explanation on why real numbers are useful in number theory?

6

“Bad” reduction of Shimura curves via dual graphs

3

Shimura datum of family of fake elliptic curves

1

is there any way to bound the number of CM points by height functions?

4

applications of Tate-Poitou duality

6

Rational Isogenies of Prime Degree