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	8	Product of Tamagawa factors cp
Δ	97384668 = 22 · 3 · 234 · 29	Discriminant
Eigenvalues	2- 3+  2  4  0 -2 -6  4	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-1867,30269]	[a1,a2,a3,a4,a6]
j	719732649848113/97384668	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	4	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	32016bd4 128064bk4 12006c3 100050bb4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4002l3

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 4002l3

-4	8	-3	5	-23	29
32016bd4	128064bk4	12006c3	100050bb4	92046bb4	116058n4

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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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