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	4002o	Isogeny class
Conductor	4002	Conductor
∏ cp	96	Product of Tamagawa factors cp
deg	5760	Modular degree for the optimal curve
Δ	-164474612208 = -1 · 24 · 312 · 23 · 292	Discriminant
Eigenvalues	2- 3- -2 -4  0 -2  6  4	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-569,-20247]	[a1,a2,a3,a4,a6]
j	-20375497153297/164474612208	j-invariant
L	2.5824310800744	L(r)(E,1)/r!
Ω	0.43040518001239	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	32016v1 128064c1 12006i1 100050m1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4002o1

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

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Quadratic twists for elliptic curve 4002o1

-4	8	-3	5	-23	29
32016v1	128064c1	12006i1	100050m1	92046bj1	116058b1

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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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