Cremona's table of elliptic curves

560 = 2⁴ · 5 · 7

Field	Data	Notes
Atkin-Lehner	2- 5+ 7+	Signs for the Atkin-Lehner involutions
Class	560c	Isogeny class
Conductor	560	Conductor
∏ cp	1	Product of Tamagawa factors cp
Δ	-56000000000 = -1 · 212 · 59 · 7	Discriminant
Eigenvalues	2- -1 5+ 7+  3  5  3 -2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-2101,39485]	[a1,a2,a3,a4,a6]
j	-250523582464/13671875	j-invariant
L	1.1025221380509	L(r)(E,1)/r!
Ω	1.1025221380509	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	35a2 2240w3 5040bk3 2800s3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 560c3

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	+	+	3	5	3	-2	6	3	4	2	-12	10	-9	12	0	8	4	0	2	1	-12	-12	-1

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Quadratic twists for elliptic curve 560c3

-4	8	-3	5	-7	-11	13
35a2	2240w3	5040bk3	2800s3	3920bc3	67760bo3	94640cx3

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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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