Cremona's table of elliptic curves

170 = 2 · 5 · 17

Field	Data	Notes
Atkin-Lehner	2+ 5+ 17-	Signs for the Atkin-Lehner involutions
Class	170b	Isogeny class
Conductor	170	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	4456448000000 = 224 · 56 · 17	Discriminant
Eigenvalues	2+ -2 5+  2  6  2 17-  8	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-4169,-20724]	[a1,a2,a3,a4,a6]
j	8010684753304969/4456448000000	j-invariant
L	0.63726065819045	L(r)(E,1)/r!
Ω	0.63726065819045	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	1360f3 5440l3 1530p3 850h3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 170b3

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 170b3

-4	8	-3	5	-7	-11	13	17	-19	-23
1360f3	5440l3	1530p3	850h3	8330k3	20570j3	28730bc3	2890i3	61370s3	89930q3

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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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