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	5200z	Isogeny class
Conductor	5200	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	-2856100000000 = -1 · 28 · 58 · 134	Discriminant
Eigenvalues	2-  2 5+  2 -4 13- -2  0	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-6908,-233188]	[a1,a2,a3,a4,a6]
Generators	[11306:424125:8]	Generators of the group modulo torsion
j	-9115564624/714025	j-invariant
L	5.3595666256254	L(r)(E,1)/r!
Ω	0.26066300758464	Real period
R	5.1403214779961	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	1300d2 20800cp2 46800dy2 1040d2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 5200z2

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	+	2	-4	-	-2	0	-6	-10	0	-10	-2	2	-6	-2	8	2	-6	8	-10	16	6	10	-2

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Quadratic twists for elliptic curve 5200z2

-4	8	-3	5	13
1300d2	20800cp2	46800dy2	1040d2	67600bx2

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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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