Cremona's table of elliptic curves

1003 = 17 · 59

Field	Data	Notes
Atkin-Lehner	17- 59+	Signs for the Atkin-Lehner involutions
Class	1003b	Isogeny class
Conductor	1003	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	48	Modular degree for the optimal curve
Δ	-17051 = -1 · 172 · 59	Discriminant
Eigenvalues	1  1  1  3  4  0 17-  7	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-8,-11]	[a1,a2,a3,a4,a6]
j	-47045881/17051	j-invariant
L	2.8315261439311	L(r)(E,1)/r!
Ω	1.4157630719656	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	16048bb1 64192bc1 9027d1 25075b1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1003b1

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	1	1	3	4	0	-	7	2	3	4	0	-3	4	6	-9	+	-10	-4	-4	-2	5	16	0	-8

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Quadratic twists for elliptic curve 1003b1

-4	8	-3	5	-7	-11	17	-59
16048bb1	64192bc1	9027d1	25075b1	49147c1	121363c1	17051b1	59177d1

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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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