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	922640625000 = 23 · 310 · 59	Discriminant
Eigenvalues	2+ 3- 5+  4  0 -2  6 -4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-1200042,506291116]	[a1,a2,a3,a4,a6]
j	16778985534208729/81000	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	3600bk7 14400bo8 150c7 90c8	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 450g8

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 450g8

-4	8	-3	5	-7	-11	13
3600bk7	14400bo8	150c7	90c8	22050be7	54450gf7	76050fb7

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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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