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	1200p	Isogeny class
Conductor	1200	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	375000000000000000 = 215 · 3 · 518	Discriminant
Eigenvalues	2- 3- 5+ -4  0 -2 -6  4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-181408,3987188]	[a1,a2,a3,a4,a6]
Generators	[4:1806:1]	Generators of the group modulo torsion
j	10316097499609/5859375000	j-invariant
L	2.7857614073248	L(r)(E,1)/r!
Ω	0.25902435054978	Real period
R	5.3774122035478	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	150c8 4800bp7 3600bk8 240b7	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1200p7

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
-	-	+	-4	0	-2	-6	4	0	-6	-8	-2	-6	-4	0	6	0	-10	-4	0	-2	-8	12	18	-2

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Quadratic twists for elliptic curve 1200p7

-4	8	-3	5	-7
150c8	4800bp7	3600bk8	240b7	58800fc8

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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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