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	4002l	Isogeny class
Conductor	4002	Conductor
∏ cp	32	Product of Tamagawa factors cp
Δ	64064016 = 24 · 32 · 232 · 292	Discriminant
Eigenvalues	2- 3+  2  4  0 -2 -6  4	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-127,341]	[a1,a2,a3,a4,a6]
j	226646274673/64064016	j-invariant
L	3.6563870656023	L(r)(E,1)/r!
Ω	1.8281935328011	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	32016bd2 128064bk2 12006c2 100050bb2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4002l2

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	4	0	-2	-6	4	-	-	8	10	10	4	-8	-6	12	-14	16	-8	2	-16	-12	10	6

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Quadratic twists for elliptic curve 4002l2

-4	8	-3	5	-23	29
32016bd2	128064bk2	12006c2	100050bb2	92046bb2	116058n2

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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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