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	8	Product of Tamagawa factors cp
Δ	4356 = 22 · 32 · 112	Discriminant
Eigenvalues	2- 3+  2 -4 11+ -6  2  4	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-22,-49]	[a1,a2,a3,a4,a6]
j	1180932193/4356	j-invariant
L	1.1021925301216	L(r)(E,1)/r!
Ω	2.2043850602432	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	528j2 2112r2 198a2 1650f2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 66b2

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 66b2

-4	8	-3	5	-7	-11	13	17	-19	-23	29	-31	37	41	-43
528j2	2112r2	198a2	1650f2	3234t2	726c2	11154h2	19074bh2	23826r2	34914w2	55506q2	63426bh2	90354a2	110946bm2	122034e2

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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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