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A122162
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Coefficient of q-series for constant term of Tate curve.
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0
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1, 23, 154, 647, 1876, 4802, 9948, 19975, 34903, 60648, 94502, 151298, 217504, 324844, 446404, 633351, 830298, 1144229, 1447250, 1931272, 2396352, 3105246, 3759604, 4821250, 5705001, 7155652, 8413300, 10373996, 11975000, 14696052
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| If w6(n) = sum a(n) q^n and w4(n) = sum 5 sigma_3(n) q^n then the Tate elliptic curve is y^2 + xy = x^3 - w4(q)x - w6(q) If |q|<1 (for either real, complex, or p-adic values) and the resulting curve is nonsingular we have an elliptic curve. The parametrization is especially useful p-adically, behaving well in characteristic 2 or 3.
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REFERENCES
| Joseph H. Silverman, "Advanced Topics in the Arithmetic of Elliptic Curves", Springer, 1994
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FORMULA
| a(n) = (5 sigma_3(n) + 7 sigma_5(n))/12, where sigma_3(n) is A001158, the sum of the cubes of the divisors of n and sigma_5(n) is A001160, the sum of the fifth powers of the divisors of n.
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CROSSREFS
| Cf. A001158, A001160.
Sequence in context: A142935 A037068 A122615 * A133253 A098713 A042022
Adjacent sequences: A122159 A122160 A122161 * A122163 A122164 A122165
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KEYWORD
| nonn
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AUTHOR
| Gene Ward Smith (genewardsmith(AT)gmail.com), Aug 22 2006
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