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	4002p	Isogeny class
Conductor	4002	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	33120	Modular degree for the optimal curve
Δ	-368184 = -1 · 23 · 3 · 232 · 29	Discriminant
Eigenvalues	2- 3-  3  1  0 -2  1 -1	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-1811224,938072696]	[a1,a2,a3,a4,a6]
j	-657113243203147908283777/368184	j-invariant
L	5.2226862643108	L(r)(E,1)/r!
Ω	0.87044771071846	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	32016w1 128064e1 12006j1 100050l1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4002p1

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
-	-	3	1	0	-2	1	-1	+	-	10	5	7	-11	-13	10	-3	10	-4	10	10	4	8	-6	0

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Quadratic twists for elliptic curve 4002p1

-4	8	-3	5	-23	29
32016w1	128064e1	12006j1	100050l1	92046bl1	116058c1

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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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