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ID: INPUT{id.yaml}

Title: >
  $j$-invariants of elliptic curves 
  over quadratic fields 
  with everywhere good reduction

Definition: >
  This table contains the $j$-invariants of elliptic curves $E/K$
  over number fields with absolute discriminant bounded by $|\Delta_K| \leq 20000$,
  such that $E$ has everywhere good reduction.
  
Parameters:
  D:
    display: $\Delta_K$
    title: discriminant of $K$
    type: Z
    
Comments:
  comment-N: >
    An elliptic curve $E$ over a number field $K$ 
    has everywhere good reduction if and only if its conductor equals $1$.
    In case the class number of $K$ is $1$, this is equivalent to
    the minimal discriminant of $E$ being $1$.
  comment-no-duplicates: >
    Rational $j$-invariants are only listed once, 
    namely for the number field of minimal absolute discriminant.

Formulas:

Programs:

References:
      
Links:
  SUE:
    title: "Tables of elliptic curves with good reduction everywhere"
    url: https://github.com/bmatschke/s-unit-equations/tree/master/elliptic-curve-tables/good-reduction-everywhere
  Wiki:
    title: "Wikipedia: j-invariant"
    url: https://en.wikipedia.org/wiki/J-invariant
    
Similar tables:
  
Keywords:
  
Tags:
- number theory
- elliptic curves
- algebraic

Data properties:
  type: C
  complete: yes, assuming GRH
  sources:
  - CITE{SUE}

Display properties:
  number-header: $j$

Numbers: INPUT{numbers.yaml}

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$j$-invariants of elliptic curves over quadratic fields with everywhere good reduction

edit on github

Numbers

$\Delta_K$

$j$

INPUT{numbers.yaml} (not shown in preview)

Definition

This table contains the $j$-invariants of elliptic curves $E/K$ over number fields with absolute discriminant bounded by $|\Delta_K| \leq 20000$, such that $E$ has everywhere good reduction.

Parameters

$\Delta_K$

— discriminant of $K$

Comments

(1)

An elliptic curve $E$ over a number field $K$ has everywhere good reduction if and only if its conductor equals $1$. In case the class number of $K$ is $1$, this is equivalent to the minimal discriminant of $E$ being $1$.

(2)

Rational $j$-invariants are only listed once, namely for the number field of minimal absolute discriminant.

Links

[1]

Tables of elliptic curves with good reduction everywhere

[2]

Wikipedia: j-invariant

Data properties

Entries are of type: complex number

Table is complete: yes, assuming GRH

Sources of data: [1]