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	5200r	Isogeny class
Conductor	5200	Conductor
∏ cp	2	Product of Tamagawa factors cp
Δ	-5624320000000000 = -1 · 218 · 510 · 133	Discriminant
Eigenvalues	2- -2 5+ -1 -3 13+ -3  4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,39792,-1906412]	[a1,a2,a3,a4,a6]
j	174196775/140608	j-invariant
L	0.47446613783191	L(r)(E,1)/r!
Ω	0.23723306891595	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	650i2 20800dd2 46800cz2 5200bi2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 5200r2

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	+	-1	-3	+	-3	4	-6	-3	1	-2	0	-10	-3	-3	15	-13	-13	0	10	4	15	6	4

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Quadratic twists for elliptic curve 5200r2

-4	8	-3	5	13
650i2	20800dd2	46800cz2	5200bi2	67600bz2

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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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