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	4002h	Isogeny class
Conductor	4002	Conductor
∏ cp	18	Product of Tamagawa factors cp
deg	864	Modular degree for the optimal curve
Δ	-23563776 = -1 · 29 · 3 · 232 · 29	Discriminant
Eigenvalues	2- 3+  1  1 -4 -2 -3  1	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,65,-91]	[a1,a2,a3,a4,a6]
Generators	[19:82:1]	Generators of the group modulo torsion
j	30342134159/23563776	j-invariant
L	4.7617105195022	L(r)(E,1)/r!
Ω	1.1889585976389	Real period
R	0.22249679158804	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	32016x1 128064bm1 12006d1 100050u1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4002h1

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	1	-4	-2	-3	1	-	+	-2	-1	-9	-5	7	6	-9	-10	-8	-2	14	-4	-8	18	-8

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Quadratic twists for elliptic curve 4002h1

-4	8	-3	5	-23	29
32016x1	128064bm1	12006d1	100050u1	92046u1	116058k1

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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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