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	1200k	Isogeny class
Conductor	1200	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	240	Modular degree for the optimal curve
Δ	-24883200 = -1 · 212 · 35 · 52	Discriminant
Eigenvalues	2- 3+ 5+ -3 -2 -1 -2  5	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,27,-243]	[a1,a2,a3,a4,a6]
j	20480/243	j-invariant
L	1.0441392649297	L(r)(E,1)/r!
Ω	1.0441392649297	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	75c1 4800cg1 3600bj1 1200r2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1200k1

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	-1	-2	5	6	10	3	-2	-8	1	2	4	10	7	-3	8	14	0	6	0	-17

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Quadratic twists for elliptic curve 1200k1

-4	8	-3	5	-7
75c1	4800cg1	3600bj1	1200r2	58800ij1

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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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