# ON THE TATE-SHAFAREVICH GROUP OF ELLIPTIC CURVES OVER ?

• Published : 2012.01.31
• 54 24

#### Abstract

Let E be an elliptic curve over $\mathbb{Q}$. Using Iwasawa theory, we give what seems to be the first general upper bound for the order of vanishing of the p-adic L-function at s = 0, and the $\mathbb{Z}_p$-corank of the Tate-Shafarevich group for all sufficiently large good ordinary primes p.

#### Keywords

good ordinary reduction;Tate-Shafarevich group;elliptic curves;Iwasawa theory

#### References

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#### Cited by

1. ON THE p-PRIMARY PART OF TATE-SHAFAREVICH GROUP OF ELLIPTIC CURVES OVER ℚ WHEN p IS SUPERSINGULAR vol.50, pp.2, 2013, https://doi.org/10.4134/BKMS.2013.50.2.407