Cremona's table of elliptic curves

66 = 2 · 3 · 11

Field	Data	Notes
Atkin-Lehner	2- 3- 11-	Signs for the Atkin-Lehner involutions
Class	66c	Isogeny class
Conductor	66	Conductor
∏ cp	10	Product of Tamagawa factors cp
Δ	1932612 = 22 · 3 · 115	Discriminant
Eigenvalues	2- 3- -4 -2 11-  4 -2  0	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-10065,-389499]	[a1,a2,a3,a4,a6]
j	112763292123580561/1932612	j-invariant
L	1.1916148156125	L(r)(E,1)/r!
Ω	0.47664592624499	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	528f3 2112d3 198e3 1650b3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 66c3

a2	a3	a5	a7	a11	a13	a17	a19	a23	a29	a31	a37	a41	a43	a47	a53	a59	a61	a67	a71	a73	a79	a83	a89	a97
-	-	-4	-2	-	4	-2	0	-6	10	-8	-2	2	4	-2	4	0	-8	-12	2	-6	10	4	10	-2

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Quadratic twists for elliptic curve 66c3

-4	8	-3	5	-7	-11	13	17	-19	-23	29	-31	37	41	-43
528f3	2112d3	198e3	1650b3	3234s3	726e3	11154q3	19074p3	23826l3	34914bf3	55506d3	63426x3	90354k3	110946v3	122034d3

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Data from Elliptic Curve Data by J. E. Cremona.
Design inspired by The Modular Forms Explorer by William Stein.

Part of Computational Number Theory
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