• Corpus ID: 119628029

# On the Selmer groups and Mordell-Weil groups of elliptic curves $y^{2} = x (x \pm p) (x \pm q)$ over imaginary quadratic number fields of class number one

@article{Li2012OnTS,
title={On the Selmer groups and Mordell-Weil groups of elliptic curves \$y^\{2\} = x (x \pm p) (x \pm q) \$ over imaginary quadratic number fields of class number one},
author={Xiumei Li},
journal={arXiv: Number Theory},
year={2012}
}
• Xiumei Li
• Published 2 July 2012
• Mathematics
• arXiv: Number Theory
Let $p$ and $q$ be odd prime numbers with $q - p = 2,$ the $\varphi -$Selmer groups, Shafarevich-Tate groups ($\varphi -$ and $2-$part) and their dual ones as well the Mordell-Weil groups of elliptic curves $y^{2} = x (x \pm p) (x \pm q)$ over imaginary quadratic number fields of class number one are determined explicitly in many cases.

## References

SHOWING 1-7 OF 7 REFERENCES

### Mordell-Weil groups and Selmer groups of two types of elliptic curves

• Mathematics, Computer Science
• 2001
It is proved that the Mordell-Weil group E(E/Q) having rank 0 and dimension 0 is proved, and the Kodaira symbol, the torsion subgroup $E(K)_{tors}$ for any number field $K$ are obtained.

### ON THE EQUATION Y(2)=(X+P)(X(2)+P(2))

• Mathematics
• 1994
textabstractIn this paper the family of elliptic curves over Q given by the equation y2 = (x + p)(x2 + p2) is studied. It is shown that for p a prime number = ±3 mod 8, the only rational solution to

### Explicit 4-descents on an elliptic curve

• Mathematics
• 1996
where f(X,Z) is a binary quartic form (or quartic for short) with integer coefficients. One wishes to know whether equation (1) has a Q-rational point and if so to exhibit one. One can often show

### A Course in p-adic Analysis

1 p-adic Numbers.- 2 Finite Extensions of the Field of p-adic Numbers.- 3 Construction of Universal p-adic Fields.- 4 Continuous Functions on Zp.- 5 Differentiation.- 6 Analytic Functions and

### Elliptic curves and their torsion subgroups over number fields of type (2

• · · · , 2), Science in China (series A)
• 2001

• 2006

### Elliptic curves and their torsion subgroups over number fields of type (2, · · · , 2)

• Science in China (series A)
• 2001