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	170d	Isogeny class
Conductor	170	Conductor
∏ cp	1	Product of Tamagawa factors cp
Δ	-12577280 = -1 · 29 · 5 · 173	Discriminant
Eigenvalues	2+  1 5-  2  0  5 17+ -1	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,22,-164]	[a1,a2,a3,a4,a6]
j	1256216039/12577280	j-invariant
L	1.1097020596077	L(r)(E,1)/r!
Ω	1.1097020596077	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	1360i2 5440a2 1530m2 850k2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 170d2

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 170d2

-4	8	-3	5	-7	-11	13	17	-19	-23
1360i2	5440a2	1530m2	850k2	8330e2	20570p2	28730r2	2890b2	61370w2	89930f2

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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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