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	1800q	Isogeny class
Conductor	1800	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	256	Modular degree for the optimal curve
Δ	-864000 = -1 · 28 · 33 · 53	Discriminant
Eigenvalues	2- 3+ 5- -4  4  4 -6 -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-15,50]	[a1,a2,a3,a4,a6]
Generators	[1:6:1]	Generators of the group modulo torsion
j	-432	j-invariant
L	2.7824559177838	L(r)(E,1)/r!
Ω	2.4918251612036	Real period
R	0.27915842181718	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	3600h1 14400t1 1800e1 1800d1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1800q1

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
-	+	-	-4	4	4	-6	-4	-4	4	0	4	-8	0	-12	-2	-12	2	8	-8	-16	-8	-8	0	-8

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Quadratic twists for elliptic curve 1800q1

-4	8	-3	5	-7
3600h1	14400t1	1800e1	1800d1	88200fh1

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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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