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	16	Product of Tamagawa factors cp
deg	192	Modular degree for the optimal curve
Δ	-135000000 = -1 · 26 · 33 · 57	Discriminant
Eigenvalues	2+ 3+ 5+ -2 -6  4 -6 -4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-192,1216]	[a1,a2,a3,a4,a6]
Generators	[-1:38:1]	Generators of the group modulo torsion
j	-1860867/320	j-invariant
L	1.4100767515259	L(r)(E,1)/r!
Ω	1.7759273414315	Real period
R	0.19849865456619	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	3600z1 14400j1 450e3 90b1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 450f1

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 450f1

-4	8	-3	5	-7	-11	13
3600z1	14400j1	450e3	90b1	22050k1	54450ee1	76050dk1

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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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