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	66a	Isogeny class
Conductor	66	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	-127552392 = -1 · 23 · 32 · 116	Discriminant
Eigenvalues	2+ 3-  0  2 11+ -4 -6 -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-41,-556]	[a1,a2,a3,a4,a6]
j	-7357983625/127552392	j-invariant
L	0.79709145734732	L(r)(E,1)/r!
Ω	0.79709145734732	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	528g4 2112e4 198b4 1650m4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 66a4

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
+	-	0	2	+	-4	-6	-4	6	6	8	-10	6	8	-6	0	0	8	-4	6	2	14	-12	-6	14

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Quadratic twists for elliptic curve 66a4

-4	8	-3	5	-7	-11	13	17	-19	-23	29	-31	37	41	-43
528g4	2112e4	198b4	1650m4	3234b4	726h4	11154bf4	19074b4	23826y4	34914o4	55506bd4	63426e4	90354v4	110946h4	122034f4

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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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