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A118778
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Total degree of the classical modular curve X_n(0). Also the degree of the classical modular polynomial.
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1
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1, 4, 6, 9, 10, 18, 14, 20, 20, 30, 22, 38, 26, 42, 40, 42, 34, 62, 38, 60, 56, 66, 46, 82, 54, 78, 66, 84, 58, 122, 62, 88, 88, 102, 84, 126, 74, 114, 104, 126, 82, 168, 86, 132, 128, 138, 94, 172, 104, 166, 136, 156, 106, 198, 132, 170, 152, 174, 118, 254, 122, 186, 172
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| This is the total degree of the classical modular curve relating j(z) to j(nz), where j is the j-invariant, or elliptic modular function. If F_n(x, y) = 0 is the equation for the curve (the classical modular equation) then F_n(x, x) is the classical modular polynomial and the sequence is also the sequence of degrees for it. When n is a prime, the degree is 2n.
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REFERENCES
| Serge Lang, ''Elliptic Functions'', Addison-Wesley, 1973
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LINKS
| T. D. Noe, Table of n, a(n) for n=1..1000
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MAPLE
| with(numtheory): degx := proc (n) # degree of the classical modular curve X0(n) local a, s; s := 0; for a in divisors(n) do if a^2 > n then s := s + 2*a*phi(igcd(a, n/a))/igcd(a, n/a) fi od; if issqr(n) then s := s+phi(sqrt(n)) fi; s end:
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CROSSREFS
| Sequence in context: A111206 A087112 A077554 * A108635 A071964 A135257
Adjacent sequences: A118775 A118776 A118777 * A118779 A118780 A118781
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KEYWORD
| nice,nonn
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AUTHOR
| Gene Ward Smith (genewardsmith(AT)gmail.com), May 22 2006
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