# Tagged Questions

**5**

votes

**1**answer

396 views

### Analogy between Jacobian of curve and Ideal class group

It is excerpt from "Algebraic Geometry Codes Basic ...

**4**

votes

**0**answers

229 views

### On Stickelberger's Theorem over function fields

Here is the setup to Stickelberger's theorem over number fields (following Washington's book Intro. to cyclotomic fields).
Let $M/\mathbb{Q}$ be a finite abelian extension with galois group $G$. ...

**2**

votes

**1**answer

429 views

### Conductor of an elliptic curve

Given any elliptic curve over $\mathbb{Q}$ of conductor $N$, by modularity of elliptic curves,
there exists a surjective morphism from $X_0(N)$ $\rightarrow$ $E$.There may be several such 'N' and ...

**3**

votes

**1**answer

991 views

### Trace of Frobenius over $F_q$

Let $q_0$ be a prime and $q$ = $q_0^n$.
Let $a(F_q/F_{q_0})$ denote any integer which is trace of Frobenius over the field $F_q$ for some elliptic curve which can be defined over $F_{q_0}$.
It is ...

**4**

votes

**1**answer

907 views

### Bound for the number of rational points on the modular curve

By Mazur's theorems (Reference:- Modular curves and the Eisenstein ideal, 1977),
we know that the only rational points of X_0(N) for N any prime > 163 are
the two cusps (o) and (oo) (|X_0(N)(Q)| = 2 ...

**6**

votes

**2**answers

715 views

### “Bad” reduction of Shimura curves via dual graphs

I have the following naive (and inexpert) question about the
reduction of Shimura curves at primes dividing the discriminant
of the underlying quaternion algebra. It requires some background
to ...