Cremona's table of elliptic curves

1003 = 17 · 59

Field	Data	Notes
Atkin-Lehner	17- 59-	Signs for the Atkin-Lehner involutions
Class	1003d	Isogeny class
Conductor	1003	Conductor
∏ cp	3	Product of Tamagawa factors cp
deg	180	Modular degree for the optimal curve
Δ	-3491443 = -1 · 17 · 593	Discriminant
Eigenvalues	2  0 -2 -2 -3  4 17- -1	Hecke eigenvalues for primes up to 20
Equation	[0,0,1,-41,135]	[a1,a2,a3,a4,a6]
Generators	[18:55:8]	Generators of the group modulo torsion
j	-7622111232/3491443	j-invariant
L	3.8300323978395	L(r)(E,1)/r!
Ω	2.3382633870212	Real period
R	0.54599386580351	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	16048w1 64192r1 9027a1 25075f1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1003d1

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
2	0	-2	-2	-3	4	-	-1	1	-6	-8	-2	0	4	12	-3	-	5	10	-4	15	6	2	-14	-19

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Quadratic twists for elliptic curve 1003d1

-4	8	-3	5	-7	-11	17	-59
16048w1	64192r1	9027a1	25075f1	49147b1	121363f1	17051d1	59177e1

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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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