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	1	Product of Tamagawa factors cp
Δ	66 = 2 · 3 · 11	Discriminant
Eigenvalues	2- 3+  2 -4 11+ -6  2  4	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-352,-2689]	[a1,a2,a3,a4,a6]
j	4824238966273/66	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	4	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	528j3 2112r3 198a3 1650f3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 66b3

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 66b3

-4	8	-3	5	-7	-11	13	17	-19	-23	29	-31	37	41	-43
528j3	2112r3	198a3	1650f3	3234t3	726c3	11154h3	19074bh3	23826r4	34914w4	55506q4	63426bh4	90354a4	110946bm4	122034e4

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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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