Geodesic
On the Selmer Group of Twists of Elliptic Curves with Q-Rational Torsion Points
Canadian journal of mathematics, Tome 40 (1988) no. 3, pp. 649-665

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(1) The symbols p and q stand for prime numbers and throughout the paper we assume that p is fixed and contained in {3, 5, 7}. Let L be an algebraic number field (i.e., L is a finite extension of Q). Then prime divisors of L dividing p (resp. q) are denoted by (resp. ). The completion of L with respect to is denoted by . Let S be a finite set of prime numbers, and let M/L be a Galois extension with abelian Galois group of exponent p. Definition. M/L is said to be little ramified outside S if for primes q ∉ S and all one has with k ∊ N and . Here ζp is a pth root of unity, u 1, ..., uk are elements in and is the normed valuation belonging to . In particular M/L is unramified at all divisors of primes q ∉ S ∪ {p}. 
Frey, G. On the Selmer Group of Twists of Elliptic Curves with Q-Rational Torsion Points. Canadian journal of mathematics, Tome 40 (1988) no. 3, pp. 649-665. doi: 10.4153/CJM-1988-028-9
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[1] 1. Frey, G., A relation between the value of the L-series of the curve y2 = x2 — k2 in s — 1 and its Selmer group, Archiv der Math. 45 (1985), 232–238. Google Scholar

[2] 2. Lutz, E., Sur l'équation y2 — x2 — Ax — B dans les corps p-adiques, J. reine angew. Math. 777 (1937), 238–247. Google Scholar

[3] 3. Mazur, B., On the arithmetic of special values of L-functions, Invent. Math. 55 (1979), 207–240. Google Scholar

[4] 4. Néron, A., Modèles minimaux des variétés abéliennes sur les corps locaux et globaux, Inst. Hautes Études Sci. Publ. Math. 21 (1964). Google Scholar

[5] 5. Roquette, P., Analytic theory of elliptic functions over local fields, Hamburger Mathematische Einzelschriften (Neue Folge), Heft 1 (Vandenhoech and Ruprecht, Güttingen, 1970). Google Scholar

[6] 6. Serre, J. P., Corps locaux (Hermann, Paris, 1962). Google Scholar

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