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	96	Product of Tamagawa factors cp
Δ	-4515625000000000000 = -1 · 212 · 518 · 172	Discriminant
Eigenvalues	2-  2 5+ -2  6 -2 17+  8	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,407787,-19998469]	[a1,a2,a3,a4,a6]
j	479958568556831351/289000000000000	j-invariant
L	3.4198995626403	L(r)(E,1)/r!
Ω	0.14249581511001	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	6800m4 27200o4 7650y4 170b4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 850h4

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 850h4

-4	8	-3	5	-7	-11	17
6800m4	27200o4	7650y4	170b4	41650cf4	102850u4	14450w4

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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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