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	50	Product of Tamagawa factors cp
deg	20	Modular degree for the optimal curve
Δ	2737152 = 210 · 35 · 11	Discriminant
Eigenvalues	2- 3- -4 -2 11-  4 -2  0	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-45,81]	[a1,a2,a3,a4,a6]
j	10091699281/2737152	j-invariant
L	1.1916148156125	L(r)(E,1)/r!
Ω	2.383229631225	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	10	Number of elements in the torsion subgroup
Twists	528f1 2112d1 198e1 1650b1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 66c1

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 66c1

-4	8	-3	5	-7	-11	13	17	-19	-23	29	-31	37	41	-43
528f1	2112d1	198e1	1650b1	3234s1	726e1	11154q1	19074p1	23826l1	34914bf1	55506d1	63426x1	90354k1	110946v1	122034d1

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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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