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
deg	4	Modular degree for the optimal curve
Δ	528 = 24 · 3 · 11	Discriminant
Eigenvalues	2- 3+  2 -4 11+ -6  2  4	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-2,-1]	[a1,a2,a3,a4,a6]
j	912673/528	j-invariant
L	1.1021925301216	L(r)(E,1)/r!
Ω	4.4087701204864	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	528j1 2112r1 198a1 1650f1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 66b1

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 66b1

-4	8	-3	5	-7	-11	13	17	-19	-23	29	-31	37	41	-43
528j1	2112r1	198a1	1650f1	3234t1	726c1	11154h1	19074bh1	23826r1	34914w1	55506q1	63426bh1	90354a1	110946bm1	122034e1

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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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