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	666d	Isogeny class
Conductor	666	Conductor
∏ cp	10	Product of Tamagawa factors cp
deg	80	Modular degree for the optimal curve
Δ	-31968 = -1 · 25 · 33 · 37	Discriminant
Eigenvalues	2- 3+ -2 -3 -5 -3 -3  5	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-26,57]	[a1,a2,a3,a4,a6]
Generators	[5:-9:1]	Generators of the group modulo torsion
j	-69426531/1184	j-invariant
L	2.6092064872888	L(r)(E,1)/r!
Ω	3.7060696314936	Real period
R	0.070403601300854	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	5328n1 21312b1 666a1 16650c1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 666d1

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 666d1

-4	8	-3	5	-7	-11	13	37
5328n1	21312b1	666a1	16650c1	32634bn1	80586b1	112554a1	24642a1

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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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