Cremona's table of elliptic curves

450 = 2 · 3² · 5²

Field	Data	Notes
Atkin-Lehner	2+ 3- 5+	Signs for the Atkin-Lehner involutions
Class	450g	Isogeny class
Conductor	450	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	-17496000000000 = -1 · 212 · 37 · 59	Discriminant
Eigenvalues	2+ 3- 5+  4  0 -2  6 -4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-3042,212116]	[a1,a2,a3,a4,a6]
j	-273359449/1536000	j-invariant
L	1.1963822281327	L(r)(E,1)/r!
Ω	0.59819111406633	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	3600bk3 14400bo3 150c3 90c3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 450g3

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 450g3

-4	8	-3	5	-7	-11	13
3600bk3	14400bo3	150c3	90c3	22050be3	54450gf3	76050fb3

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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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