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	16	Product of Tamagawa factors cp
Δ	-722500 = -1 · 22 · 54 · 172	Discriminant
Eigenvalues	2+ -2 5- -2 -2 -6 17- -8	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,12,38]	[a1,a2,a3,a4,a6]
Generators	[-1:5:1]	Generators of the group modulo torsion
j	214921799/722500	j-invariant
L	0.8289341482393	L(r)(E,1)/r!
Ω	2.0204645502541	Real period
R	0.10256727198394	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	1360j2 5440c2 1530k2 850g2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 170a2

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 170a2

-4	8	-3	5	-7	-11	13	17	-19	-23
1360j2	5440c2	1530k2	850g2	8330d2	20570o2	28730x2	2890c2	61370x2	89930d2

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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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