Cremona's table of elliptic curves

3003 = 3 · 7 · 11 · 13

Field	Data	Notes
Atkin-Lehner	3+ 7+ 11- 13+	Signs for the Atkin-Lehner involutions
Class	3003a	Isogeny class
Conductor	3003	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	8741423691 = 38 · 7 · 114 · 13	Discriminant
Eigenvalues	1 3+  2 7+ 11- 13+  6 -4	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-689,-5610]	[a1,a2,a3,a4,a6]
j	36254831403673/8741423691	j-invariant
L	1.896010432754	L(r)(E,1)/r!
Ω	0.94800521637699	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	48048cr3 9009d4 75075bs3 21021p3	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 3003a3

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	+	-	+	6	-4	0	6	-4	-2	6	0	4	6	-8	10	-4	8	6	4	12	-2	-10

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Quadratic twists for elliptic curve 3003a3

-4	-3	5	-7	-11	13
48048cr3	9009d4	75075bs3	21021p3	33033o3	39039l3

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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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