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	5200bf	Isogeny class
Conductor	5200	Conductor
∏ cp	3	Product of Tamagawa factors cp
Δ	594068800000000 = 212 · 58 · 135	Discriminant
Eigenvalues	2- -1 5- -2 -2 13+  2  0	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-39333,-2750963]	[a1,a2,a3,a4,a6]
Generators	[-108:475:1]	Generators of the group modulo torsion
j	4206161920/371293	j-invariant
L	2.8078229407083	L(r)(E,1)/r!
Ω	0.34091813522637	Real period
R	2.7453540411238	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	325d2 20800ea2 46800es2 5200w1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 5200bf2

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	9	5	-2	-8	12	-1	8	11	0	-13	-2	-12	6	-15	4	-10	-8

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Quadratic twists for elliptic curve 5200bf2

-4	8	-3	5	13
325d2	20800ea2	46800es2	5200w1	67600cz2

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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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