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	4002j	Isogeny class
Conductor	4002	Conductor
∏ cp	36	Product of Tamagawa factors cp
Δ	574696932864 = 29 · 3 · 232 · 294	Discriminant
Eigenvalues	2- 3+ -2  2 -2 -2  4 -4	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-7789,-265309]	[a1,a2,a3,a4,a6]
Generators	[-53:72:1]	Generators of the group modulo torsion
j	52260349338689617/574696932864	j-invariant
L	4.2184822237972	L(r)(E,1)/r!
Ω	0.50853096797043	Real period
R	0.92171426444148	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	32016bb2 128064bo2 12006f2 100050y2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4002j2

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	4	-4	-	+	4	-4	-2	-8	0	2	0	8	8	0	-10	-14	6	-12	18

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Quadratic twists for elliptic curve 4002j2

-4	8	-3	5	-23	29
32016bb2	128064bo2	12006f2	100050y2	92046y2	116058o2

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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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