Cremona's table of elliptic curves

737 = 11 · 67

Field	Data	Notes
Atkin-Lehner	11- 67-	Signs for the Atkin-Lehner involutions
Class	737a	Isogeny class
Conductor	737	Conductor
∏ cp	12	Product of Tamagawa factors cp
deg	672	Modular degree for the optimal curve
Δ	-4403471083 = -1 · 114 · 673	Discriminant
Eigenvalues	-2  2 -2 -2 11- -2  7  3	Hecke eigenvalues for primes up to 20
Equation	[0,-1,1,406,-686]	[a1,a2,a3,a4,a6]
Generators	[106:1105:1]	Generators of the group modulo torsion
j	7382979842048/4403471083	j-invariant
L	1.4537684160815	L(r)(E,1)/r!
Ω	0.8056517670274	Real period
R	0.15037187649174	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	11792a1 47168a1 6633c1 18425e1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 737a1

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	2	-2	-2	-	-2	7	3	-7	-9	-2	-9	4	-6	-1	6	-7	6	-	0	-11	-16	12	15	-16

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Quadratic twists for elliptic curve 737a1

-4	8	-3	5	-7	-11	13	-67
11792a1	47168a1	6633c1	18425e1	36113h1	8107a1	124553a1	49379c1

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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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