Cremona's table of elliptic curves

5642 = 2 · 7 · 13 · 31

Field	Data	Notes
Atkin-Lehner	2+ 7+ 13+ 31+	Signs for the Atkin-Lehner involutions
Class	5642b	Isogeny class
Conductor	5642	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	10080	Modular degree for the optimal curve
Δ	-631155825664 = -1 · 210 · 76 · 132 · 31	Discriminant
Eigenvalues	2+  2  2 7+ -4 13+  4 -4	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-3549,88445]	[a1,a2,a3,a4,a6]
Generators	[218:3011:1]	Generators of the group modulo torsion
j	-4945758439372633/631155825664	j-invariant
L	4.2689971383658	L(r)(E,1)/r!
Ω	0.88503093501715	Real period
R	2.4117784867504	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	45136j1 50778z1 39494n1 73346z1	Quadratic twists by: -4 -3 -7 13

Hecke Eigenvalues for elliptic curve 5642b1

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

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Quadratic twists for elliptic curve 5642b1

-4	-3	-7	13
45136j1	50778z1	39494n1	73346z1

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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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