Cremona's table of elliptic curves

660 = 2² · 3 · 5 · 11

Field	Data	Notes
Atkin-Lehner	2- 3- 5+ 11+	Signs for the Atkin-Lehner involutions
Class	660c	Isogeny class
Conductor	660	Conductor
∏ cp	2	Product of Tamagawa factors cp
Δ	170069856000 = 28 · 3 · 53 · 116	Discriminant
Eigenvalues	2- 3- 5+ -4 11+ -4 -6  2	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-1556,-13356]	[a1,a2,a3,a4,a6]
Generators	[378:1155:8]	Generators of the group modulo torsion
j	1628514404944/664335375	j-invariant
L	2.2071066960177	L(r)(E,1)/r!
Ω	0.78771809748832	Real period
R	5.6037983716642	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	2640p4 10560n4 1980f4 3300c4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 660c4

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

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Quadratic twists for elliptic curve 660c4

-4	8	-3	5	-7	-11	13
2640p4	10560n4	1980f4	3300c4	32340p4	7260p4	111540bo4

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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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