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	8	Product of Tamagawa factors cp
deg	13824	Modular degree for the optimal curve
Δ	1664000000000 = 216 · 59 · 13	Discriminant
Eigenvalues	2- -2 5+ -4  6 13+  6 -2	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-13008,-572012]	[a1,a2,a3,a4,a6]
j	3803721481/26000	j-invariant
L	0.89444373547214	L(r)(E,1)/r!
Ω	0.44722186773607	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	650j1 20800de1 46800do1 1040g1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 5200s1

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 5200s1

-4	8	-3	5	13
650j1	20800de1	46800do1	1040g1	67600cf1

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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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