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	660b	Isogeny class
Conductor	660	Conductor
∏ cp	6	Product of Tamagawa factors cp
Δ	464640 = 28 · 3 · 5 · 112	Discriminant
Eigenvalues	2- 3+ 5+  0 11- -4 -2  2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-76,280]	[a1,a2,a3,a4,a6]
Generators	[-6:22:1]	Generators of the group modulo torsion
j	192143824/1815	j-invariant
L	1.8332170917685	L(r)(E,1)/r!
Ω	2.9740851833395	Real period
R	0.41093131248963	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	2640s2 10560ba2 1980c2 3300m2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 660b2

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	-	-4	-2	2	-8	-4	-4	-2	-12	8	-4	-10	4	6	12	0	-16	6	-2	18	-2

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Quadratic twists for elliptic curve 660b2

-4	8	-3	5	-7	-11	13
2640s2	10560ba2	1980c2	3300m2	32340bo2	7260a2	111540l2

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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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