Cremona's table of elliptic curves

4200 = 2³ · 3 · 5² · 7

Field	Data	Notes
Atkin-Lehner	2- 3- 5+ 7+	Signs for the Atkin-Lehner involutions
Class	4200x	Isogeny class
Conductor	4200	Conductor
∏ cp	192	Product of Tamagawa factors cp
Δ	142884000000 = 28 · 36 · 56 · 72	Discriminant
Eigenvalues	2- 3- 5+ 7+  0 -6  2  4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-6308,189888]	[a1,a2,a3,a4,a6]
Generators	[118:-1050:1]	Generators of the group modulo torsion
j	6940769488/35721	j-invariant
L	4.1702653482076	L(r)(E,1)/r!
Ω	1.0382105228542	Real period
R	0.33473183395911	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	8400f2 33600c2 12600m2 168b2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4200x2

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	-6	2	4	4	-10	-8	-6	-2	4	-8	10	12	-2	-12	-12	14	-8	-12	-2	-10

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Quadratic twists for elliptic curve 4200x2

-4	8	-3	5	-7
8400f2	33600c2	12600m2	168b2	29400cr2

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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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