Cremona's table of elliptic curves

1411 = 17 · 83

Field	Data	Notes
Atkin-Lehner	17+ 83+	Signs for the Atkin-Lehner involutions
Class	1411b	Isogeny class
Conductor	1411	Conductor
∏ cp	2	Product of Tamagawa factors cp
Δ	23987 = 172 · 83	Discriminant
Eigenvalues	-1 -2  0 -2 -2  2 17+  4	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-443,-3626]	[a1,a2,a3,a4,a6]
Generators	[26:38:1]	Generators of the group modulo torsion
j	9616037784625/23987	j-invariant
L	1.1588152690293	L(r)(E,1)/r!
Ω	1.0406233875837	Real period
R	2.2271559199148	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	22576d2 90304e2 12699b2 35275e2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1411b2

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
-1	-2	0	-2	-2	2	+	4	2	6	2	6	-6	4	8	-6	4	-2	-12	12	-16	8	+	-18	0

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Quadratic twists for elliptic curve 1411b2

-4	8	-3	5	-7	17	-83
22576d2	90304e2	12699b2	35275e2	69139b2	23987c2	117113b2

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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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