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	4002q	Isogeny class
Conductor	4002	Conductor
∏ cp	120	Product of Tamagawa factors cp
deg	5760	Modular degree for the optimal curve
Δ	-3260780423424 = -1 · 28 · 33 · 23 · 295	Discriminant
Eigenvalues	2- 3- -1  0 -3 -5 -4  4	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-1326,-88956]	[a1,a2,a3,a4,a6]
Generators	[468:9858:1]	Generators of the group modulo torsion
j	-257854523348449/3260780423424	j-invariant
L	5.646168802565	L(r)(E,1)/r!
Ω	0.33962208640697	Real period
R	0.13854047946593	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	32016o1 128064o1 12006a1 100050g1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4002q1

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	0	-3	-5	-4	4	-	-	-3	-1	3	-2	-6	-2	-5	3	-7	-15	0	10	-14	-6	6

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Quadratic twists for elliptic curve 4002q1

-4	8	-3	5	-23	29
32016o1	128064o1	12006a1	100050g1	92046be1	116058e1

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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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