Cremona's table of elliptic curves

850 = 2 · 5² · 17

Field	Data	Notes
Atkin-Lehner	2- 5+ 17+	Signs for the Atkin-Lehner involutions
Class	850h	Isogeny class
Conductor	850	Conductor
∏ cp	48	Product of Tamagawa factors cp
Δ	69632000000000000 = 224 · 512 · 17	Discriminant
Eigenvalues	2-  2 5+ -2  6 -2 17+  8	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-104213,-2590469]	[a1,a2,a3,a4,a6]
j	8010684753304969/4456448000000	j-invariant
L	3.4198995626403	L(r)(E,1)/r!
Ω	0.28499163022002	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	6800m3 27200o3 7650y3 170b3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 850h3

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	6	-2	+	8	6	-6	2	-2	-6	4	-12	-6	0	2	-8	-6	-2	-10	-12	6	-2

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Quadratic twists for elliptic curve 850h3

-4	8	-3	5	-7	-11	17
6800m3	27200o3	7650y3	170b3	41650cf3	102850u3	14450w3

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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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