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	450c	Isogeny class
Conductor	450	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	64	Modular degree for the optimal curve
Δ	-1093500 = -1 · 22 · 37 · 53	Discriminant
Eigenvalues	2+ 3- 5- -2 -2 -6  2  0	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-27,81]	[a1,a2,a3,a4,a6]
Generators	[0:9:1]	Generators of the group modulo torsion
j	-24389/12	j-invariant
L	1.4111308700949	L(r)(E,1)/r!
Ω	2.5697855356915	Real period
R	0.13728099587454	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	3600bm1 14400cg1 150a1 450a1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 450c1

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

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Quadratic twists for elliptic curve 450c1

-4	8	-3	5	-7	-11	13
3600bm1	14400cg1	150a1	450a1	22050cn1	54450gz1	76050fw1

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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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