# Explicit Determination of Non-Trivial Torsion Structures of Elliptic Curves over Quadratic Number Fields

@inproceedings{Reichert1985ExplicitDO, title={Explicit Determination of Non-Trivial Torsion Structures of Elliptic Curves over Quadratic Number Fields}, author={M. A. Reichert}, booktitle={European Conference on Computer Algebra}, year={1985} }

- Published 1985 in European Conference on Computer Algebra
DOI:10.1007/3-540-15984-3_318

We determine equations of the modular curves XX(N) for N = 11,13,14,15,16, 17 and 18. Except for N = 17, these are the only existing elliptic or hyperelliptic XX(N). Applying these X^N), we calculate tables of elliptic curves E over quadratic fields K with torsion groups of one of the following isomorphism types: Etor(K) s Z/mZ, m = 11,13, 14, 15, 16 and 18.Â

#### From This Paper

##### Topics from this paper.

#### Citations

##### Publications citing this paper.

Showing 1-10 of 15 extracted citations

## Families of elliptic curves over cubic number fields with prescribed torsion subgroups

View 9 Excerpts

Highly Influenced

## Torsion groups of elliptic curves over quadratic fields

View 7 Excerpts

Highly Influenced

## Constructing Elliptic Curves with Prescribed Torsion over Finite Fields

View 9 Excerpts

Highly Influenced

## Finding Suitable Curvesfor the Elliptic Curve Method of Factorizationa

View 4 Excerpts

Highly Influenced

## Finding Suitable Curves for the Elliptic Curve Method of Factorization

View 3 Excerpts

Highly Influenced

## Torsion subgroups of elliptic curves over number fields

View 1 Excerpt

## Torsion and Tamagawa Numbers

View 1 Excerpt

#### References

##### Publications referenced by this paper.

Showing 1-10 of 15 references

## An algorithm for finding a minimal Weierstrass equation for an elliptic curve,

View 4 Excerpts

Highly Influenced

## Les points exceptionnels sur les cubiques planes du premier genre

View 5 Excerpts

Highly Influenced

## REICHERT, Explizite Bestimmung nichttrivialer Torsionsstrukturen elliptischer Kurven Ã¼ber quadratischen ZahlkÃ¶rpern

View 3 Excerpts

Highly Influenced

## Conjectured Diophantine Estimates on Elliptic Curves, Progress in Mathematics, vol

View 1 Excerpt

## R

View 2 Excerpts

## Corps euclidiens, unitÃ©s exceptionnelles et courbes elliptiques,

View 1 Excerpt

## Certain torsion points on elliptic curves defined over quadratic fields

## Certain torsion points on elliptic curves defined over quadratic fields," J

View 1 Excerpt

## Torsion points on elliptic curves over a global field,

View 3 Excerpts

## Rational points of modular curves," in Modular Functions of One Variable V

View 1 Excerpt