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	850k	Isogeny class
Conductor	850	Conductor
∏ cp	108	Product of Tamagawa factors cp
Δ	-196520000000 = -1 · 29 · 57 · 173	Discriminant
Eigenvalues	2- -1 5+ -2  0 -5 17- -1	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,562,-20469]	[a1,a2,a3,a4,a6]
Generators	[225:-3513:1]	Generators of the group modulo torsion
j	1256216039/12577280	j-invariant
L	2.71151214062	L(r)(E,1)/r!
Ω	0.49627384801088	Real period
R	0.050590201348026	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	6800s2 27200v2 7650q2 170d2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 850k2

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
-	-1	+	-2	0	-5	-	-1	-6	-9	-1	4	-6	-2	9	9	3	-7	-14	3	-11	8	0	-9	7

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Quadratic twists for elliptic curve 850k2

-4	8	-3	5	-7	-11	17
6800s2	27200v2	7650q2	170d2	41650bp2	102850f2	14450s2

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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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