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	4002r	Isogeny class
Conductor	4002	Conductor
∏ cp	342	Product of Tamagawa factors cp
deg	16416	Modular degree for the optimal curve
Δ	-158312380760064 = -1 · 219 · 39 · 232 · 29	Discriminant
Eigenvalues	2- 3- -1 -3  0 -2  5 -5	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-27706,1873124]	[a1,a2,a3,a4,a6]
Generators	[68:518:1]	Generators of the group modulo torsion
j	-2352048005459422369/158312380760064	j-invariant
L	5.4651561099841	L(r)(E,1)/r!
Ω	0.56638625635601	Real period
R	0.028213941363083	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	32016p1 128064p1 12006b1 100050h1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4002r1

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	-3	0	-2	5	-5	-	-	-6	-7	-9	1	3	10	-11	-6	-4	-6	-6	4	16	-6	0

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Quadratic twists for elliptic curve 4002r1

-4	8	-3	5	-23	29
32016p1	128064p1	12006b1	100050h1	92046bg1	116058f1

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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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