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	12	Product of Tamagawa factors cp
Δ	-176418 = -1 · 2 · 36 · 112	Discriminant
Eigenvalues	2+ 3-  0  2 11+ -4 -6 -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,4,20]	[a1,a2,a3,a4,a6]
j	9938375/176418	j-invariant
L	0.79709145734732	L(r)(E,1)/r!
Ω	2.391274372042	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	6	Number of elements in the torsion subgroup
Twists	528g2 2112e2 198b2 1650m2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 66a2

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 66a2

-4	8	-3	5	-7	-11	13	17	-19	-23	29	-31	37	41	-43
528g2	2112e2	198b2	1650m2	3234b2	726h2	11154bf2	19074b2	23826y2	34914o2	55506bd2	63426e2	90354v2	110946h2	122034f2

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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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