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	5642d	Isogeny class
Conductor	5642	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	10080	Modular degree for the optimal curve
Δ	-4335140561024 = -1 · 27 · 7 · 132 · 315	Discriminant
Eigenvalues	2+  1 -1 7+ -6 13- -6  2	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-3294,-124080]	[a1,a2,a3,a4,a6]
j	-3950981143258969/4335140561024	j-invariant
L	0.6041663398725	L(r)(E,1)/r!
Ω	0.30208316993625	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	45136l1 50778bc1 39494d1 73346t1	Quadratic twists by: -4 -3 -7 13

Hecke Eigenvalues for elliptic curve 5642d1

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	+	-6	-	-6	2	3	-3	+	2	-2	2	3	10	4	2	-3	-6	-11	-3	-11	9	6

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Quadratic twists for elliptic curve 5642d1

-4	-3	-7	13
45136l1	50778bc1	39494d1	73346t1

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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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