Cremona's table of elliptic curves

3471 = 3 · 13 · 89

Field	Data	Notes
Atkin-Lehner	3- 13+ 89-	Signs for the Atkin-Lehner involutions
Class	3471d	Isogeny class
Conductor	3471	Conductor
∏ cp	10	Product of Tamagawa factors cp
deg	720	Modular degree for the optimal curve
Δ	68319693 = 310 · 13 · 89	Discriminant
Eigenvalues	0 3-  2  1 -2 13+ -7  1	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,-177,758]	[a1,a2,a3,a4,a6]
Generators	[-6:40:1]	Generators of the group modulo torsion
j	616729673728/68319693	j-invariant
L	3.8695868999181	L(r)(E,1)/r!
Ω	1.8914571972106	Real period
R	0.20458231387021	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	55536u1 10413e1 86775h1 45123i1	Quadratic twists by: -4 -3 5 13

Hecke Eigenvalues for elliptic curve 3471d1

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	+	-7	1	-4	-4	0	10	3	-10	-10	-11	-1	2	2	6	-4	1	9	-	2

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Quadratic twists for elliptic curve 3471d1

-4	-3	5	13
55536u1	10413e1	86775h1	45123i1

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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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