Abstract
In this paper we construct elliptic curves defined over the rationals with arbitrarily large Iwasawa λ-invariants for primes p satisfying \({p\leq7}\) or p = 13. We use this to obtain that the p-rank of the Tate-Shafarevich group can be arbitrarily large for such primes p.
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Matsuno, K. Construction of elliptic curves with large Iwasawa \({\lambda}\) -invariants and large Tate-Shafarevich groups. manuscripta math. 122, 289–304 (2007). https://doi.org/10.1007/s00229-006-0068-9
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DOI: https://doi.org/10.1007/s00229-006-0068-9