Cremona's table of elliptic curves

15582 = 2 · 3 · 7² · 53

Field	Data	Notes
Atkin-Lehner	2- 3- 7- 53-	Signs for the Atkin-Lehner involutions
Class	15582y	Isogeny class
Conductor	15582	Conductor
∏ cp	312	Product of Tamagawa factors cp
deg	239616	Modular degree for the optimal curve
Δ	-569491034575970304 = -1 · 213 · 34 · 78 · 533	Discriminant
Eigenvalues	2- 3- -1 7- -1  0  7  4	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,132789,31178097]	[a1,a2,a3,a4,a6]
Generators	[522:-15843:1]	Generators of the group modulo torsion
j	2201007734483039/4840593924096	j-invariant
L	8.4583063489227	L(r)(E,1)/r!
Ω	0.20205773044678	Real period
R	0.1341693593539	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	124656cq1 46746j1 2226h1	Quadratic twists by: -4 -3 -7

Hecke Eigenvalues for elliptic curve 15582y1

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
-	-	-1	-	-1	0	7	4	-7	-8	-9	-4	-6	5	-12	-	5	6	-8	-4	2	-15	4	9	-1

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Quadratic twists for elliptic curve 15582y1

-4	-3	-7
124656cq1	46746j1	2226h1

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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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