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	66b	Isogeny class
Conductor	66	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	-2371842 = -1 · 2 · 34 · 114	Discriminant
Eigenvalues	2- 3+  2 -4 11+ -6  2  4	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-12,-81]	[a1,a2,a3,a4,a6]
j	-192100033/2371842	j-invariant
L	1.1021925301216	L(r)(E,1)/r!
Ω	1.1021925301216	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	528j4 2112r4 198a4 1650f4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 66b4

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

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Quadratic twists for elliptic curve 66b4

-4	8	-3	5	-7	-11	13	17	-19	-23	29	-31	37	41	-43
528j4	2112r4	198a4	1650f4	3234t4	726c4	11154h4	19074bh4	23826r3	34914w3	55506q3	63426bh3	90354a3	110946bm3	122034e3

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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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