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	4200c	Isogeny class
Conductor	4200	Conductor
∏ cp	11	Product of Tamagawa factors cp
deg	66528	Modular degree for the optimal curve
Δ	-1992689780862412800 = -1 · 211 · 39 · 52 · 711	Discriminant
Eigenvalues	2+ 3+ 5+ 7-  2  3  5  4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,197672,58827532]	[a1,a2,a3,a4,a6]
j	16683494528422270/38919722282469	j-invariant
L	2.0083543470269	L(r)(E,1)/r!
Ω	0.18257766791153	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	8400t1 33600cw1 12600ca1 4200bd1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4200c1

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
+	+	+	-	2	3	5	4	5	9	-5	-10	1	-3	-12	-11	5	9	4	-4	6	14	-5	-6	18

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Quadratic twists for elliptic curve 4200c1

-4	8	-3	5	-7
8400t1	33600cw1	12600ca1	4200bd1	29400bm1

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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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