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	4002a	Isogeny class
Conductor	4002	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	201304602 = 2 · 38 · 232 · 29	Discriminant
Eigenvalues	2+ 3+  0 -4  0  6  0  0	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-270,1458]	[a1,a2,a3,a4,a6]
Generators	[1:34:1]	Generators of the group modulo torsion
j	2189403771625/201304602	j-invariant
L	2.0323378049724	L(r)(E,1)/r!
Ω	1.7378841541179	Real period
R	1.1694322663319	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	32016be2 128064bd2 12006r2 100050ck2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4002a2

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

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Quadratic twists for elliptic curve 4002a2

-4	8	-3	5	-23	29
32016be2	128064bd2	12006r2	100050ck2	92046a2	116058bb2

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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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