Cremona's table of elliptic curves

1200 = 2⁴ · 3 · 5²

Field	Data	Notes
Atkin-Lehner	2+ 3+ 5-	Signs for the Atkin-Lehner involutions
Class	1200d	Isogeny class
Conductor	1200	Conductor
∏ cp	3	Product of Tamagawa factors cp
deg	672	Modular degree for the optimal curve
Δ	-349920000 = -1 · 28 · 37 · 54	Discriminant
Eigenvalues	2+ 3+ 5-  5  6 -3 -2 -1	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-233,-1563]	[a1,a2,a3,a4,a6]
j	-8780800/2187	j-invariant
L	1.8085875064925	L(r)(E,1)/r!
Ω	0.60286250216418	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	600e1 4800ct1 3600x1 1200h1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1200d1

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
+	+	-	5	6	-3	-2	-1	2	6	-3	-6	4	-11	10	-8	6	3	1	12	10	8	6	-16	-7

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Quadratic twists for elliptic curve 1200d1

-4	8	-3	5	-7
600e1	4800ct1	3600x1	1200h1	58800er1

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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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