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	5600a	Isogeny class
Conductor	5600	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	1152960200000000 = 29 · 58 · 78	Discriminant
Eigenvalues	2+  0 5+ 7+  0  2 -2  8	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-26675,-378250]	[a1,a2,a3,a4,a6]
Generators	[-119:1054:1]	Generators of the group modulo torsion
j	262389836808/144120025	j-invariant
L	3.6844714953716	L(r)(E,1)/r!
Ω	0.39939311639667	Real period
R	4.6125876287164	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	5600d2 11200bt4 50400cv3 1120o3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 5600a3

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
+	0	+	+	0	2	-2	8	-8	6	0	2	-6	-8	8	2	8	-2	-8	0	-10	-16	-16	10	14

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Quadratic twists for elliptic curve 5600a3

-4	8	-3	5	-7
5600d2	11200bt4	50400cv3	1120o3	39200e3

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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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