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	4200w	Isogeny class
Conductor	4200	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	3072	Modular degree for the optimal curve
Δ	-45018750000 = -1 · 24 · 3 · 58 · 74	Discriminant
Eigenvalues	2- 3- 5+ 7+  0  2 -6 -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,217,-10062]	[a1,a2,a3,a4,a6]
Generators	[459:9849:1]	Generators of the group modulo torsion
j	4499456/180075	j-invariant
L	4.2224368470386	L(r)(E,1)/r!
Ω	0.54617675158342	Real period
R	3.8654490829181	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	8400e1 33600b1 12600l1 840b1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4200w1

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	0	-6	6	4	-8	-14	-4	-2	-12	-12	-10	8	4	6	14

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Quadratic twists for elliptic curve 4200w1

-4	8	-3	5	-7
8400e1	33600b1	12600l1	840b1	29400cp1

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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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