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	450d	Isogeny class
Conductor	450	Conductor
∏ cp	1	Product of Tamagawa factors cp
Δ	-56953125000 = -1 · 23 · 36 · 510	Discriminant
Eigenvalues	2+ 3- 5+ -2  3  4 -3  5	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-28242,1833916]	[a1,a2,a3,a4,a6]
j	-349938025/8	j-invariant
L	1.0312291893723	L(r)(E,1)/r!
Ω	1.0312291893723	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	3600bi4 14400bh4 50b4 450b2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 450d4

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	3	4	-3	5	6	0	2	-2	3	4	12	6	0	2	13	-12	-11	-10	-9	-15	-2

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Quadratic twists for elliptic curve 450d4

-4	8	-3	5	-7	-11	13
3600bi4	14400bh4	50b4	450b2	22050bm4	54450fq4	76050ek4

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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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