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	850g	Isogeny class
Conductor	850	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	-11289062500 = -1 · 22 · 510 · 172	Discriminant
Eigenvalues	2-  2 5+  2 -2  6 17+ -8	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,312,4781]	[a1,a2,a3,a4,a6]
j	214921799/722500	j-invariant
L	3.6143168643974	L(r)(E,1)/r!
Ω	0.90357921609935	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	6800n2 27200m2 7650u2 170a2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 850g2

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	-2	6	+	-8	2	6	-2	-6	2	4	-4	10	0	-10	-8	14	-10	-14	4	6	14

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Quadratic twists for elliptic curve 850g2

-4	8	-3	5	-7	-11	17
6800n2	27200m2	7650u2	170a2	41650cd2	102850v2	14450x2

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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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