Cremona's table of elliptic curves

2450 = 2 · 5² · 7²

Field	Data	Notes
Atkin-Lehner	2- 5+ 7-	Signs for the Atkin-Lehner involutions
Class	2450y	Isogeny class
Conductor	2450	Conductor
∏ cp	72	Product of Tamagawa factors cp
Δ	46118408000000 = 29 · 56 · 78	Discriminant
Eigenvalues	2- -2 5+ 7-  0 -4  6 -2	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-3344888,2354339392]	[a1,a2,a3,a4,a6]
Generators	[1012:1944:1]	Generators of the group modulo torsion
j	2251439055699625/25088	j-invariant
L	3.3629720129559	L(r)(E,1)/r!
Ω	0.44809782432921	Real period
R	0.41694417681503	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	19600cp6 78400cc6 22050bi6 98a6	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2450y6

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

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Quadratic twists for elliptic curve 2450y6

-4	8	-3	5	-7
19600cp6	78400cc6	22050bi6	98a6	350d6

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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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