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	4002f	Isogeny class
Conductor	4002	Conductor
∏ cp	48	Product of Tamagawa factors cp
Δ	5563780852176 = 24 · 34 · 236 · 29	Discriminant
Eigenvalues	2+ 3-  2  0  2 -6 -8 -2	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-200195,34459886]	[a1,a2,a3,a4,a6]
Generators	[252:46:1]	Generators of the group modulo torsion
j	887320005345582835753/5563780852176	j-invariant
L	3.5133929378841	L(r)(E,1)/r!
Ω	0.67846860424996	Real period
R	0.43153469886399	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	32016m2 128064u2 12006n2 100050bl2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4002f2

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	0	2	-6	-8	-2	-	+	8	0	-6	-6	4	-6	-4	-8	-4	-8	-10	-2	12	8	12

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Quadratic twists for elliptic curve 4002f2

-4	8	-3	5	-23	29
32016m2	128064u2	12006n2	100050bl2	92046g2	116058x2

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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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