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	1200a	Isogeny class
Conductor	1200	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	128	Modular degree for the optimal curve
Δ	-750000 = -1 · 24 · 3 · 56	Discriminant
Eigenvalues	2+ 3+ 5+  0 -4  2 -2  4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,17,-38]	[a1,a2,a3,a4,a6]
Generators	[18:76:1]	Generators of the group modulo torsion
j	2048/3	j-invariant
L	2.2570981600125	L(r)(E,1)/r!
Ω	1.5077809545821	Real period
R	2.9939337715511	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	600d1 4800cb1 3600k1 48a4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1200a1

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	-4	2	-2	4	-8	6	-8	-6	-6	4	0	2	-4	-2	-4	-8	-10	8	-4	-6	-2

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Quadratic twists for elliptic curve 1200a1

-4	8	-3	5	-7
600d1	4800cb1	3600k1	48a4	58800dm1

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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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