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	450f	Isogeny class
Conductor	450	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	9610839843750 = 2 · 39 · 512	Discriminant
Eigenvalues	2+ 3+ 5+ -2 -6  4 -6 -4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-5442,-39034]	[a1,a2,a3,a4,a6]
Generators	[-41:358:1]	Generators of the group modulo torsion
j	57960603/31250	j-invariant
L	1.4100767515259	L(r)(E,1)/r!
Ω	0.59197578047717	Real period
R	1.1909919273971	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	3600z4 14400j4 450e2 90b4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 450f4

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

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Quadratic twists for elliptic curve 450f4

-4	8	-3	5	-7	-11	13
3600z4	14400j4	450e2	90b4	22050k4	54450ee4	76050dk4

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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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