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	12	Product of Tamagawa factors cp
Δ	12708699174 = 2 · 33 · 234 · 292	Discriminant
Eigenvalues	2- 3- -2 -4  0 -2  6  4	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-242219,-45904101]	[a1,a2,a3,a4,a6]
j	1571623248760107387697/12708699174	j-invariant
L	2.5824310800744	L(r)(E,1)/r!
Ω	0.2152025900062	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	4	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	32016v4 128064c4 12006i4 100050m4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4002o3

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 4002o3

-4	8	-3	5	-23	29
32016v4	128064c4	12006i4	100050m4	92046bj4	116058b4

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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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