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	8	Product of Tamagawa factors cp
deg	896	Modular degree for the optimal curve
Δ	-6267132 = -1 · 22 · 34 · 23 · 292	Discriminant
Eigenvalues	2+ 3+  0 -4  0  6  0  0	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,20,124]	[a1,a2,a3,a4,a6]
Generators	[-2:10:1]	Generators of the group modulo torsion
j	817400375/6267132	j-invariant
L	2.0323378049724	L(r)(E,1)/r!
Ω	1.7378841541179	Real period
R	0.58471613316593	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	32016be1 128064bd1 12006r1 100050ck1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4002a1

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 4002a1

-4	8	-3	5	-23	29
32016be1	128064bd1	12006r1	100050ck1	92046a1	116058bb1

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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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