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	3003i	Isogeny class
Conductor	3003	Conductor
∏ cp	7	Product of Tamagawa factors cp
deg	728	Modular degree for the optimal curve
Δ	-2189187 = -1 · 37 · 7 · 11 · 13	Discriminant
Eigenvalues	2 3-  0 7- 11+ 13-  6  6	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,-98,-415]	[a1,a2,a3,a4,a6]
j	-105154048000/2189187	j-invariant
L	5.2997688547448	L(r)(E,1)/r!
Ω	0.75710983639212	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	48048bk1 9009n1 75075c1 21021c1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 3003i1

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	-	+	-	6	6	4	-1	3	6	5	-2	-4	2	0	-1	8	5	-6	-6	-9	-6	-13

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Quadratic twists for elliptic curve 3003i1

-4	-3	5	-7	-11	13
48048bk1	9009n1	75075c1	21021c1	33033u1	39039v1

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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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