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	8	Product of Tamagawa factors cp
Δ	-289000000000000 = -1 · 212 · 512 · 172	Discriminant
Eigenvalues	2+ -2 5+  2  6  2 17-  8	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,16311,-159988]	[a1,a2,a3,a4,a6]
j	479958568556831351/289000000000000	j-invariant
L	0.63726065819045	L(r)(E,1)/r!
Ω	0.31863032909523	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	1360f4 5440l4 1530p4 850h4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 170b4

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 170b4

-4	8	-3	5	-7	-11	13	17	-19	-23
1360f4	5440l4	1530p4	850h4	8330k4	20570j4	28730bc4	2890i4	61370s4	89930q4

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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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