Cremona's table of elliptic curves

18060 = 2² · 3 · 5 · 7 · 43

Field	Data	Notes
Atkin-Lehner	2- 3- 5+ 7- 43-	Signs for the Atkin-Lehner involutions
Class	18060k	Isogeny class
Conductor	18060	Conductor
∏ cp	216	Product of Tamagawa factors cp
deg	27648	Modular degree for the optimal curve
Δ	3135289323600 = 24 · 312 · 52 · 73 · 43	Discriminant
Eigenvalues	2- 3- 5+ 7-  0 -4  0 -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-3701,14724]	[a1,a2,a3,a4,a6]
Generators	[-23:297:1]	Generators of the group modulo torsion
j	350492173533184/195955582725	j-invariant
L	5.6281770078019	L(r)(E,1)/r!
Ω	0.69047090187408	Real period
R	1.3585358901502	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	6	Number of elements in the torsion subgroup
Twists	72240bf1 54180x1 90300a1 126420t1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 18060k1

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	0	-4	0	-6	2	8	-6	-	12	6	6	2	-4	-6	14	8	0	-6	8

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Quadratic twists for elliptic curve 18060k1

-4	-3	5	-7
72240bf1	54180x1	90300a1	126420t1

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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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