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	4200b	Isogeny class
Conductor	4200	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	3840	Modular degree for the optimal curve
Δ	-44108290800 = -1 · 24 · 38 · 52 · 75	Discriminant
Eigenvalues	2+ 3+ 5+ 7+ -3 -2  4 -2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,632,7837]	[a1,a2,a3,a4,a6]
Generators	[-2:81:1]	Generators of the group modulo torsion
j	69683121920/110270727	j-invariant
L	2.9372224158833	L(r)(E,1)/r!
Ω	0.7762053229075	Real period
R	0.9460197995297	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	8400z1 33600ci1 12600bu1 4200bf1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4200b1

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
+	+	+	+	-3	-2	4	-2	9	-7	10	-5	-8	7	10	-10	-6	-8	13	1	-4	-13	-14	6	2

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Quadratic twists for elliptic curve 4200b1

-4	8	-3	5	-7
8400z1	33600ci1	12600bu1	4200bf1	29400bq1

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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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