Cremona's table of elliptic curves

4002 = 2 · 3 · 23 · 29

Field	Data	Notes
Atkin-Lehner	2- 3- 23+ 29-	Signs for the Atkin-Lehner involutions
Class	4002n	Isogeny class
Conductor	4002	Conductor
∏ cp	24	Product of Tamagawa factors cp
Δ	9940968 = 23 · 34 · 232 · 29	Discriminant
Eigenvalues	2- 3-  0  4  0 -2  4  8	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-1233,-16767]	[a1,a2,a3,a4,a6]
j	207317019156625/9940968	j-invariant
L	4.8340312202009	L(r)(E,1)/r!
Ω	0.80567187003348	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	32016u2 128064b2 12006h2 100050n2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4002n2

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

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Quadratic twists for elliptic curve 4002n2

-4	8	-3	5	-23	29
32016u2	128064b2	12006h2	100050n2	92046bd2	116058a2

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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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