Cremona's table of elliptic curves

666 = 2 · 3² · 37

Field	Data	Notes
Atkin-Lehner	2- 3- 37-	Signs for the Atkin-Lehner involutions
Class	666f	Isogeny class
Conductor	666	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	147556443852 = 22 · 39 · 374	Discriminant
Eigenvalues	2- 3- -2  0  4  6 -6  8	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-5441,-151995]	[a1,a2,a3,a4,a6]
j	24431916147913/202409388	j-invariant
L	2.2246573039018	L(r)(E,1)/r!
Ω	0.55616432597546	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	5328v4 21312m3 222c4 16650i3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 666f3

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	0	4	6	-6	8	0	6	4	-	6	-8	-8	-6	4	-2	-12	0	10	-12	4	10	-6

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Quadratic twists for elliptic curve 666f3

-4	8	-3	5	-7	-11	13	37
5328v4	21312m3	222c4	16650i3	32634ce3	80586q3	112554b3	24642g3

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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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