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	4002k	Isogeny class
Conductor	4002	Conductor
∏ cp	24	Product of Tamagawa factors cp
deg	8064	Modular degree for the optimal curve
Δ	-5921086039488 = -1 · 26 · 314 · 23 · 292	Discriminant
Eigenvalues	2- 3+ -2 -2  2 -2  0  4	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-5429,-195685]	[a1,a2,a3,a4,a6]
Generators	[119:868:1]	Generators of the group modulo torsion
j	-17696534894747857/5921086039488	j-invariant
L	3.9008067845009	L(r)(E,1)/r!
Ω	0.27345571688622	Real period
R	2.3774762198663	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	32016z1 128064bp1 12006g1 100050v1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4002k1

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

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Quadratic twists for elliptic curve 4002k1

-4	8	-3	5	-23	29
32016z1	128064bp1	12006g1	100050v1	92046x1	116058p1

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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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