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	4200q	Isogeny class
Conductor	4200	Conductor
∏ cp	64	Product of Tamagawa factors cp
Δ	1764000000 = 28 · 32 · 56 · 72	Discriminant
Eigenvalues	2- 3+ 5+ 7-  0  2 -6 -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-308,612]	[a1,a2,a3,a4,a6]
Generators	[-8:50:1]	Generators of the group modulo torsion
j	810448/441	j-invariant
L	3.2231581324676	L(r)(E,1)/r!
Ω	1.2980485254096	Real period
R	0.62076996147941	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	8400r2 33600cr2 12600q2 168a2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4200q2

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

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Quadratic twists for elliptic curve 4200q2

-4	8	-3	5	-7
8400r2	33600cr2	12600q2	168a2	29400dz2

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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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