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	4200t	Isogeny class
Conductor	4200	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	4800	Modular degree for the optimal curve
Δ	-2583393750000 = -1 · 24 · 310 · 58 · 7	Discriminant
Eigenvalues	2- 3+ 5- 7+ -1  4  2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-1708,82537]	[a1,a2,a3,a4,a6]
Generators	[16:243:1]	Generators of the group modulo torsion
j	-88218880/413343	j-invariant
L	3.0655925269207	L(r)(E,1)/r!
Ω	0.70489441059538	Real period
R	1.0872523887412	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	8400bf1 33600dg1 12600y1 4200n1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4200t1

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	4	2	-4	-3	-1	-6	-3	0	5	4	6	-4	-4	-5	-1	10	-1	14	-8	-14

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Quadratic twists for elliptic curve 4200t1

-4	8	-3	5	-7
8400bf1	33600dg1	12600y1	4200n1	29400em1

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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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