Cremona's table of elliptic curves

1800 = 2³ · 3² · 5²

Field	Data	Notes
Atkin-Lehner	2- 3- 5+	Signs for the Atkin-Lehner involutions
Class	1800s	Isogeny class
Conductor	1800	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	34992000000 = 210 · 37 · 56	Discriminant
Eigenvalues	2- 3- 5+  0 -4  2  2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-14475,-670250]	[a1,a2,a3,a4,a6]
Generators	[-69:4:1]	Generators of the group modulo torsion
j	28756228/3	j-invariant
L	2.900443842633	L(r)(E,1)/r!
Ω	0.4352588700035	Real period
R	1.6659303477317	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	3600k4 14400x3 600d4 72a3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1800s3

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
-	-	+	0	-4	2	2	-4	-8	-6	8	-6	6	-4	0	-2	-4	-2	4	-8	-10	-8	-4	6	-2

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Quadratic twists for elliptic curve 1800s3

-4	8	-3	5	-7
3600k4	14400x3	600d4	72a3	88200ha4

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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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