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	3003h	Isogeny class
Conductor	3003	Conductor
∏ cp	100	Product of Tamagawa factors cp
deg	5600	Modular degree for the optimal curve
Δ	-1561102682139 = -1 · 310 · 75 · 112 · 13	Discriminant
Eigenvalues	0 3- -1 7- 11+ 13+ -4  7	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,-32781,2274347]	[a1,a2,a3,a4,a6]
Generators	[147:-809:1]	Generators of the group modulo torsion
j	-3895861901277528064/1561102682139	j-invariant
L	3.2077715535878	L(r)(E,1)/r!
Ω	0.83179269811272	Real period
R	0.038564555337718	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	48048bh1 9009i1 75075e1 21021e1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 3003h1

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	-	-1	-	+	+	-4	7	-3	3	-3	4	-10	1	1	-3	4	8	-6	-14	-11	-7	-5	-7	-13

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Quadratic twists for elliptic curve 3003h1

-4	-3	5	-7	-11	13
48048bh1	9009i1	75075e1	21021e1	33033v1	39039t1

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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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