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	666c	Isogeny class
Conductor	666	Conductor
∏ cp	12	Product of Tamagawa factors cp
Δ	-221556222 = -1 · 2 · 37 · 373	Discriminant
Eigenvalues	2+ 3-  0 -1 -3 -1  3 -7	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-1332,19062]	[a1,a2,a3,a4,a6]
Generators	[21:-6:1]	Generators of the group modulo torsion
j	-358667682625/303918	j-invariant
L	1.6232934653678	L(r)(E,1)/r!
Ω	1.7584042022306	Real period
R	0.69237215054504	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	3	Number of elements in the torsion subgroup
Twists	5328t2 21312j2 222a2 16650bw2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 666c2

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
+	-	0	-1	-3	-1	3	-7	-3	0	2	-	6	-4	-6	-9	0	-10	2	-12	5	2	-3	3	2

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Quadratic twists for elliptic curve 666c2

-4	8	-3	5	-7	-11	13	37
5328t2	21312j2	222a2	16650bw2	32634bd2	80586bf2	112554p2	24642o2

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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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