Cremona's table of elliptic curves

1476 = 2² · 3² · 41

Field	Data	Notes
Atkin-Lehner	2- 3- 41+	Signs for the Atkin-Lehner involutions
Class	1476a	Isogeny class
Conductor	1476	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	192	Modular degree for the optimal curve
Δ	-22954752 = -1 · 28 · 37 · 41	Discriminant
Eigenvalues	2- 3-  0 -2  1 -2  1 -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-120,-556]	[a1,a2,a3,a4,a6]
Generators	[13:9:1]	Generators of the group modulo torsion
j	-1024000/123	j-invariant
L	2.6790439234162	L(r)(E,1)/r!
Ω	0.71640444380792	Real period
R	1.8697845515699	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	5904k1 23616e1 492a1 36900f1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1476a1

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	-2	1	-2	1	-4	6	-5	-3	-3	+	-7	3	-10	0	1	2	-3	-11	6	-4	-6	8

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Quadratic twists for elliptic curve 1476a1

-4	8	-3	5	-7	41
5904k1	23616e1	492a1	36900f1	72324o1	60516h1

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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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