Cremona's table of elliptic curves

1411 = 17 · 83

Field	Data	Notes
Atkin-Lehner	17+ 83+	Signs for the Atkin-Lehner involutions
Class	1411a	Isogeny class
Conductor	1411	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	76	Modular degree for the optimal curve
Δ	-1411 = -1 · 17 · 83	Discriminant
Eigenvalues	0 -2 -3  4 -4  4 17+  2	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,3,0]	[a1,a2,a3,a4,a6]
Generators	[0:0:1]	Generators of the group modulo torsion
j	2097152/1411	j-invariant
L	1.50896605111	L(r)(E,1)/r!
Ω	2.7252691987514	Real period
R	0.55369431093314	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	22576e1 90304f1 12699a1 35275d1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1411a1

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	-3	4	-4	4	+	2	4	4	0	-8	2	-6	-6	-6	-15	12	2	3	6	4	+	-12	-7

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Quadratic twists for elliptic curve 1411a1

-4	8	-3	5	-7	17	-83
22576e1	90304f1	12699a1	35275d1	69139a1	23987a1	117113a1

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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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