|
Search: id:A118778
|
|
|
| A118778 |
|
Total degree of the classical modular curve X_n(0). Also the degree of the classical modular polynomial. |
|
+0
1
|
|
| 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; listen)
|
|
|
OFFSET
|
1,2
|
|
|
COMMENT
|
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.
|
|
REFERENCES
|
Serge Lang, ''Elliptic Functions'', Addison-Wesley, 1973
|
|
LINKS
|
T. D. Noe, Table of n, a(n) for n=1..1000
|
|
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:
|
|
CROSSREFS
|
Sequence in context: A111206 A087112 A077554 this_sequence A108635 A071964 A135257
Adjacent sequences: A118775 A118776 A118777 this_sequence A118779 A118780 A118781
|
|
KEYWORD
|
nice,nonn
|
|
AUTHOR
|
Gene Ward Smith (genewardsmith(AT)gmail.com), May 22 2006
|
|
|
Search completed in 0.002 seconds
|
