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	4200i	Isogeny class
Conductor	4200	Conductor
∏ cp	12	Product of Tamagawa factors cp
deg	1920	Modular degree for the optimal curve
Δ	-3543750000 = -1 · 24 · 34 · 58 · 7	Discriminant
Eigenvalues	2+ 3+ 5- 7- -3 -2  0  2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-708,8037]	[a1,a2,a3,a4,a6]
Generators	[42:225:1]	Generators of the group modulo torsion
j	-6288640/567	j-invariant
L	3.125294173731	L(r)(E,1)/r!
Ω	1.3740995124565	Real period
R	0.18953589516865	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	8400bd1 33600dt1 12600cn1 4200y1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4200i1

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	0	2	7	-3	-6	-3	0	5	2	2	-10	-8	-9	9	-8	-1	14	-6	-2

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Quadratic twists for elliptic curve 4200i1

-4	8	-3	5	-7
8400bd1	33600dt1	12600cn1	4200y1	29400ch1

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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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