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	170a	Isogeny class
Conductor	170	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	16	Modular degree for the optimal curve
Δ	6800 = 24 · 52 · 17	Discriminant
Eigenvalues	2+ -2 5- -2 -2 -6 17- -8	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-8,6]	[a1,a2,a3,a4,a6]
Generators	[0:2:1]	Generators of the group modulo torsion
j	47045881/6800	j-invariant
L	0.8289341482393	L(r)(E,1)/r!
Ω	4.0409291005083	Real period
R	0.20513454396788	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	1360j1 5440c1 1530k1 850g1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 170a1

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 170a1

-4	8	-3	5	-7	-11	13	17	-19	-23
1360j1	5440c1	1530k1	850g1	8330d1	20570o1	28730x1	2890c1	61370x1	89930d1

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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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