mersenneforum.org - View Single Post - Elliptic-curve L-function question

fivemack · 2010-08-22, 14:52

I have a mug, on which is written

'If E is X0(11): y^2+y = x^3-x^2-10x-20, then the $L_E$ is $q \prod_{n=1}^\infty (1-q^n)^2 (1-q^{11n})^2$ ', with a few hundred terms expanded. And, indeed, the product agrees with the coefficients of

ellan(ellinit([0,-1,1,-10,-20]),100)

Are there any other elliptic curves whose L-functions are such nice infinite products?

2010-08-22, 14:52	#1
fivemack (loop (#_fork)) Feb 2006 Cambridge, England 3³·239 Posts	Elliptic-curve L-function question I have a mug, on which is written 'If E is X0(11): y^2+y = x^3-x^2-10x-20, then the $L_E$ is $q \prod_{n=1}^\infty (1-q^n)^2 (1-q^{11n})^2$ ', with a few hundred terms expanded. And, indeed, the product agrees with the coefficients of ellan(ellinit([0,-1,1,-10,-20]),100) Are there any other elliptic curves whose L-functions are such nice infinite products?