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A276173
Number of solutions to the congruence y^2 + x*y + y == x^3 + 4*x - 6 (mod p) as p runs through the primes.
3
3, 5, 5, 6, 11, 17, 11, 17, 23, 35, 35, 35, 35, 35, 59, 47, 65, 53, 71, 71, 71, 71, 89, 95, 107, 101, 107, 95, 107, 107, 143, 113, 119, 125, 167, 143, 161, 179, 179, 185, 191, 161, 167, 179, 215, 179, 215, 215, 209, 233, 239, 215, 251, 269, 239, 263, 281, 287, 287, 287
OFFSET
1,1
COMMENTS
This elliptic curve corresponds to a weight 2 newform which is an eta-quotient, namely, eta(t)*eta(2t)*eta(7t)*eta(14t), see Theorem 2 in Martin & Ono.
LINKS
Yves Martin and Ken Ono, Eta-Quotients and Elliptic Curves, Proc. Amer. Math. Soc. 125, No 11 (1997), 3169-3176.
FORMULA
a(n) gives the number of solutions of the congruence y^2 + x*y + y == x^3 + 4*x - 6 (mod prime(n)), n >= 1.
EXAMPLE
The first nonnegative complete residue system {0, 1, ..., prime(n)-1} is used.
The solutions (x, y) of y^2 + x*y + y == x^3 + 4*x - 6 (mod prime(n)) begin:
n, prime(n), a(n): solutions (x, y)
1, 2, 3: (0, 0), (0, 1), (1, 1)
2, 3, 5: (0, 0), (0, 2), (1, 2),
(2, 1), (2, 2)
3, 5, 5: (1, 4), (2, 0), (2, 2),
(4, 2), (4, 3)
4, 7, 6: (1, 6), (2, 2), (3, 1),
(3, 2), (5, 3), (5, 5)
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Sep 10 2016
STATUS
approved