Cremona's table of elliptic curves

18240 = 2⁶ · 3 · 5 · 19

Field	Data	Notes
Atkin-Lehner	2+ 3+ 5+ 19+	Signs for the Atkin-Lehner involutions
Class	18240c	Isogeny class
Conductor	18240	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	27648	Modular degree for the optimal curve
Δ	-29047652352000 = -1 · 224 · 36 · 53 · 19	Discriminant
Eigenvalues	2+ 3+ 5+  2  0 -2  0 19+	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-1441,260641]	[a1,a2,a3,a4,a6]
Generators	[415:8424:1]	Generators of the group modulo torsion
j	-1263214441/110808000	j-invariant
L	4.1227051513055	L(r)(E,1)/r!
Ω	0.54585924530106	Real period
R	3.7763445309346	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	18240cn1 570f1 54720bs1 91200cy1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 18240c1

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	0	-2	0	+	0	6	2	-2	0	-8	0	-6	6	-2	4	0	14	2	-6	-12	-10

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Quadratic twists for elliptic curve 18240c1

-4	8	-3	5
18240cn1	570f1	54720bs1	91200cy1

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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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