Cremona's table of elliptic curves

1003 = 17 · 59

Field	Data	Notes
Atkin-Lehner	17+ 59+	Signs for the Atkin-Lehner involutions
Class	1003a	Isogeny class
Conductor	1003	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	36	Modular degree for the optimal curve
Δ	-1003 = -1 · 17 · 59	Discriminant
Eigenvalues	0  2 -2  2 -5  2 17+ -5	Hecke eigenvalues for primes up to 20
Equation	[0,-1,1,1,1]	[a1,a2,a3,a4,a6]
Generators	[1:1:1]	Generators of the group modulo torsion
j	32768/1003	j-invariant
L	2.6089060570307	L(r)(E,1)/r!
Ω	3.7193019737596	Real period
R	0.70145045372414	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	16048u1 64192n1 9027e1 25075g1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1003a1

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	-2	2	-5	2	+	-5	-5	-6	8	2	-6	-2	6	-11	+	-1	-8	-6	13	4	6	10	3

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Quadratic twists for elliptic curve 1003a1

-4	8	-3	5	-7	-11	17	-59
16048u1	64192n1	9027e1	25075g1	49147f1	121363h1	17051a1	59177a1

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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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