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	666a	Isogeny class
Conductor	666	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	240	Modular degree for the optimal curve
Δ	-23304672 = -1 · 25 · 39 · 37	Discriminant
Eigenvalues	2+ 3+  2 -3  5 -3  3  5	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-231,-1315]	[a1,a2,a3,a4,a6]
j	-69426531/1184	j-invariant
L	1.2231192487799	L(r)(E,1)/r!
Ω	0.61155962438995	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	5328l1 21312d1 666d1 16650bp1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 666a1

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	-3	5	-3	3	5	3	0	4	-	6	4	-4	-3	14	-14	12	12	13	6	-7	-1	-12

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Quadratic twists for elliptic curve 666a1

-4	8	-3	5	-7	-11	13	37
5328l1	21312d1	666d1	16650bp1	32634f1	80586v1	112554o1	24642l1

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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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