Cremona's table of elliptic curves

5600 = 2⁵ · 5² · 7

Field	Data	Notes
Atkin-Lehner	2- 5+ 7-	Signs for the Atkin-Lehner involutions
Class	5600r	Isogeny class
Conductor	5600	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	4608	Modular degree for the optimal curve
Δ	-56000000000 = -1 · 212 · 59 · 7	Discriminant
Eigenvalues	2- -1 5+ 7- -1  1 -1  0	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-7533,254437]	[a1,a2,a3,a4,a6]
Generators	[87:500:1]	Generators of the group modulo torsion
j	-738763264/875	j-invariant
L	3.2417881409176	L(r)(E,1)/r!
Ω	1.1129709985134	Real period
R	0.36409171322161	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	5600l1 11200cj1 50400bf1 1120a1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 5600r1

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	1	-1	0	4	-1	-10	8	2	-4	11	-4	-8	10	-4	-12	-6	-7	-8	-6	-1

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Quadratic twists for elliptic curve 5600r1

-4	8	-3	5	-7
5600l1	11200cj1	50400bf1	1120a1	39200br1

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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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