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	5200x	Isogeny class
Conductor	5200	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	288	Modular degree for the optimal curve
Δ	83200 = 28 · 52 · 13	Discriminant
Eigenvalues	2- -1 5+  2  2 13- -2  0	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-13,17]	[a1,a2,a3,a4,a6]
Generators	[1:2:1]	Generators of the group modulo torsion
j	40960/13	j-invariant
L	3.3998964895297	L(r)(E,1)/r!
Ω	3.1581435961949	Real period
R	0.53827452520304	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	1300c1 20800ch1 46800dx1 5200bd1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 5200x1

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	+	2	2	-	-2	0	-3	-7	6	-4	-8	-1	0	1	-4	-1	6	8	14	-5	0	-14	4

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Quadratic twists for elliptic curve 5200x1

-4	8	-3	5	13
1300c1	20800ch1	46800dx1	5200bd1	67600bt1

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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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