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	4002b	Isogeny class
Conductor	4002	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	7392	Modular degree for the optimal curve
Δ	-397480312836 = -1 · 22 · 311 · 23 · 293	Discriminant
Eigenvalues	2+ 3+  1  4 -3  1  6  6	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-6612,-211932]	[a1,a2,a3,a4,a6]
j	-31976054253232201/397480312836	j-invariant
L	1.5871122860468	L(r)(E,1)/r!
Ω	0.26451871434113	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	32016bg1 128064x1 12006q1 100050cn1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4002b1

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
+	+	1	4	-3	1	6	6	+	-	-1	3	1	6	4	-10	-3	7	3	9	2	12	-10	12	-6

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Quadratic twists for elliptic curve 4002b1

-4	8	-3	5	-23	29
32016bg1	128064x1	12006q1	100050cn1	92046c1	116058bc1

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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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