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	32	Product of Tamagawa factors cp
Δ	-3771495156250000 = -1 · 24 · 510 · 176	Discriminant
Eigenvalues	2-  2 5+ -2  6 -2 17+  8	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-61838,6589531]	[a1,a2,a3,a4,a6]
j	-1673672305534489/241375690000	j-invariant
L	3.4198995626403	L(r)(E,1)/r!
Ω	0.42748744533003	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	6800m2 27200o2 7650y2 170b2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 850h2

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 850h2

-4	8	-3	5	-7	-11	17
6800m2	27200o2	7650y2	170b2	41650cf2	102850u2	14450w2

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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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