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	18060g	Isogeny class
Conductor	18060	Conductor
∏ cp	24	Product of Tamagawa factors cp
deg	73728	Modular degree for the optimal curve
Δ	477867600 = 24 · 34 · 52 · 73 · 43	Discriminant
Eigenvalues	2- 3- 5+ 7+  0  4 -4  4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-398221,96591404]	[a1,a2,a3,a4,a6]
Generators	[359:165:1]	Generators of the group modulo torsion
j	436493012606522097664/29866725	j-invariant
L	5.6744228715044	L(r)(E,1)/r!
Ω	0.91689197184662	Real period
R	1.0314597294881	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	72240bs1 54180q1 90300q1 126420o1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 18060g1

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	-4	4	0	-10	6	-8	6	+	-8	-10	6	2	-4	2	-2	16	4	-6	-16

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Quadratic twists for elliptic curve 18060g1

-4	-3	5	-7
72240bs1	54180q1	90300q1	126420o1

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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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