This paper studies the family of elliptic curves \(E_{m}: X^{3}+Y^{3}=m\) where \(m\) is a cubefree integer. Assuming the Generalized Rieman Hypothesis, the average rank of \(E_{m}\) 's with even analytic rank is proved to be \(\leqslant 5 / 2\), asymptotically. We also obtain some results for the c
A Formula for the Root Number of a Family of Elliptic Curves
β Scribed by E. Liverance
- Publisher
- Elsevier Science
- Year
- 1995
- Tongue
- English
- Weight
- 578 KB
- Volume
- 51
- Category
- Article
- ISSN
- 0022-314X
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
We compute the ,-Selmer group for a family of elliptic curves, where , is an isogeny of degree 5, then find a practical formula for the Cassels Tate pairing on the ,-Selmer groups and use it to show that a particular family of elliptic curves have non-trivial 5-torsion in their Shafarevich Tate grou
## Abstract A fitting formula is proposed to approximate the falloff curves of the pressureβ and temperatureβdependent unimolecular reaction rate constants. Compared with the widely used Troe's formula, the present expression has the potential to substantially reduce the computation time in its eva
This paper presents a compact differential formula for the first derivative of a unit quaternion curve defined on SO(3) or S3. The formula provides a convenient way to compute the angular velocity of a rotating 3D solid. We demonstrate the effectiveness of this formula by deriving the differential p