Cremona's table of elliptic curves

5200 = 2⁴ · 5² · 13

Field	Data	Notes
Atkin-Lehner	2+ 5+ 13+	Signs for the Atkin-Lehner involutions
Class	5200d	Isogeny class
Conductor	5200	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	2880	Modular degree for the optimal curve
Δ	-9505100800 = -1 · 210 · 52 · 135	Discriminant
Eigenvalues	2+  2 5+ -3 -1 13+  5  4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,272,4272]	[a1,a2,a3,a4,a6]
Generators	[6:78:1]	Generators of the group modulo torsion
j	86614940/371293	j-invariant
L	4.8892684144481	L(r)(E,1)/r!
Ω	0.92557931420322	Real period
R	2.6411936499775	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	2600i1 20800di1 46800u1 5200l1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 5200d1

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	+	-3	-1	+	5	4	-2	-3	-5	6	-8	-6	-1	-11	-3	-5	9	-8	2	4	-3	6	4

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Quadratic twists for elliptic curve 5200d1

-4	8	-3	5	13
2600i1	20800di1	46800u1	5200l1	67600n1

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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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