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	5200s	Isogeny class
Conductor	5200	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	-676000000000000 = -1 · 214 · 512 · 132	Discriminant
Eigenvalues	2- -2 5+ -4  6 13+  6 -2	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-5008,-1260012]	[a1,a2,a3,a4,a6]
j	-217081801/10562500	j-invariant
L	0.89444373547214	L(r)(E,1)/r!
Ω	0.22361093386804	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	650j2 20800de2 46800do2 1040g2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 5200s2

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	+	-4	6	+	6	-2	6	-6	-2	-2	-6	2	-12	-6	-6	2	-4	6	10	4	0	-6	-2

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Quadratic twists for elliptic curve 5200s2

-4	8	-3	5	13
650j2	20800de2	46800do2	1040g2	67600cf2

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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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