Cremona's table of elliptic curves

1003 = 17 · 59

Field	Data	Notes
Atkin-Lehner	17- 59+	Signs for the Atkin-Lehner involutions
Class	1003c	Isogeny class
Conductor	1003	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	384	Modular degree for the optimal curve
Δ	-59354531 = -1 · 172 · 593	Discriminant
Eigenvalues	-1  3  1  1  0 -2 17-  5	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,63,-332]	[a1,a2,a3,a4,a6]
j	28066748319/59354531	j-invariant
L	2.0552525422591	L(r)(E,1)/r!
Ω	1.0276262711296	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	16048bf1 64192bh1 9027c1 25075a1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1003c1

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	3	1	1	0	-2	-	5	4	-9	10	-8	-3	10	12	3	+	8	-8	8	-6	-9	-16	-14	2

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Quadratic twists for elliptic curve 1003c1

-4	8	-3	5	-7	-11	17	-59
16048bf1	64192bh1	9027c1	25075a1	49147d1	121363b1	17051c1	59177c1

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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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