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In the Martin and Ono reference, in Theorem 2, this elliptic curve appears in the fourth row, starting with conductor 20, as a strong Weil curve for the weight 2 newform (eta(2*z)*eta(10*z))^2, symbolically 2^2 10^2, with Im(z) > 0, and the Dedekind eta function. See A030205 which gives the q-expansion (q = exp(2*Pi*i*z)) of exp(-Pi*i*z)*(eta(z)*eta(5*z))^2. For the q-expansion of (eta(2*z)*eta(10*z))^2 one has interspersed 0s0's: 0, 1, 0, -2, 0, -1, 0, 2, 0, 1, 0, 0, 0, 2, 0, 2, 0, -6, ... This modular cusp form of weight 2 appears as the 39th entry in Martin's Table I.

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In the Martin and Ono reference, in Theorem 2, this elliptic curve appears in the fourth row, starting with conductor 20, as a strong Weil curve for the weight 2 newform (eta(2*z)*eta(10*z))^2, symbolically 2^2 10^2, with Im(z) > 0, and the Dedekind eta function. See A030205 which gives the q-expansion (q = exp(2*Pi*Ii*z)) of exp(-Pi*Ii*z)*(eta(z)*eta(5*z))^2. For the q-expansion of (eta(2*z)*eta(10*z))^2 one has interspersed 0s: 0, 1, 0, -2, 0, -1, 0, 2, 0, 1, 0, 0, 0, 2, 0, 2, 0, -6, ... This modular cusp form of weight 2 appears as the 39th entry in Martin's table Table I.

The discriminant of this elliptic curve is -400 = -2^4*5^2 (bad primes 2 and 5, also the prime divisors of the conductor).

a(n) gives the number of solutions of the congruence y^2 == x^3 + x^2 + 4*x + 4 (mod prime(n)), n >= 1.

a(n) gives also the number of solutions of the congruence y^2 == x^3 + x^2 - x (mod prime(n)), n >= 1.

The solutions (x, y) of y^2 == x^3 + x^2 + 4*x + 4 (mod prime(n)) begin:

The solutions (x, y) of y^2 == x^3 + x^2 - x (mod prime(n)) begin:

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Seiichi Manyama, <a href="/A272207/b272207.txt">Table of n, a(n) for n = 1..10000</a>

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In the Martin and Ono reference, in Theorem 2, this elliptic curve appears in the fourth row, starting with conductor 20, as a strong Weil curve for the weight 2 newform (eta(2*z)*eta(10*z))^2, symbolically 2^2 10^2, with Im(z) > 0, and the Dedekind eta function. See A030205 which gives the q-expansion (q = exp(2*Pi*I*z)) of exp(-Pi*I*z)*(eta(z)*eta(5*z))^2. For the q-expansion of (eta(2*z)*eta(10*z))^2 one has interspersed 0s: 0, 1, 0, -2, 0, -1, 0, 2, 0, 1, 0, 0, 0, 2, 0, 2, 0, -6, ... This modular cusp form of weight 2 appears as 39th entry in Martin's table I.

This modular cusp form of weight 2 appears as 39th entry in Martin's table I.

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