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	3003d	Isogeny class
Conductor	3003	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	6954210586323 = 35 · 72 · 112 · 136	Discriminant
Eigenvalues	1 3+  0 7- 11+ 13+  0 -8	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-63000,6058881]	[a1,a2,a3,a4,a6]
j	27653883672870015625/6954210586323	j-invariant
L	1.4576126225897	L(r)(E,1)/r!
Ω	0.72880631129485	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	48048cf2 9009k2 75075bf2 21021i2	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 3003d2

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	+	0	-	+	+	0	-8	8	4	2	10	10	-6	-12	-2	12	-2	10	-4	10	-14	-4	-12	2

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Quadratic twists for elliptic curve 3003d2

-4	-3	5	-7	-11	13
48048cf2	9009k2	75075bf2	21021i2	33033g2	39039i2

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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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