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	12	Product of Tamagawa factors cp
deg	48	Modular degree for the optimal curve
Δ	-39600 = -1 · 24 · 32 · 52 · 11	Discriminant
Eigenvalues	2- 3+ 5+  0 11- -4 -2  2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-1,10]	[a1,a2,a3,a4,a6]
Generators	[1:3:1]	Generators of the group modulo torsion
j	-16384/2475	j-invariant
L	1.8332170917685	L(r)(E,1)/r!
Ω	2.9740851833395	Real period
R	0.20546565624481	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	2640s1 10560ba1 1980c1 3300m1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 660b1

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 660b1

-4	8	-3	5	-7	-11	13
2640s1	10560ba1	1980c1	3300m1	32340bo1	7260a1	111540l1

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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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