Cremona's table of elliptic curves

15540 = 2² · 3 · 5 · 7 · 37

Field	Data	Notes
Atkin-Lehner	2- 3+ 5- 7+ 37+	Signs for the Atkin-Lehner involutions
Class	15540f	Isogeny class
Conductor	15540	Conductor
∏ cp	12	Product of Tamagawa factors cp
deg	6720	Modular degree for the optimal curve
Δ	931467600 = 24 · 35 · 52 · 7 · 372	Discriminant
Eigenvalues	2- 3+ 5- 7+ -2  2  2  4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-505,-3950]	[a1,a2,a3,a4,a6]
Generators	[-15:5:1]	Generators of the group modulo torsion
j	891943960576/58216725	j-invariant
L	4.2712355296281	L(r)(E,1)/r!
Ω	1.0110690612425	Real period
R	1.408158187328	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	62160cu1 46620o1 77700x1 108780x1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 15540f1

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

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Quadratic twists for elliptic curve 15540f1

-4	-3	5	-7
62160cu1	46620o1	77700x1	108780x1

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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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