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	170c	Isogeny class
Conductor	170	Conductor
∏ cp	21	Product of Tamagawa factors cp
deg	84	Modular degree for the optimal curve
Δ	-4456448000 = -1 · 221 · 53 · 17	Discriminant
Eigenvalues	2-  1 5+  2  0 -1 17+ -1	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,399,-919]	[a1,a2,a3,a4,a6]
j	7023836099951/4456448000	j-invariant
L	1.8469013549656	L(r)(E,1)/r!
Ω	0.79152915212813	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	3	Number of elements in the torsion subgroup
Twists	1360d1 5440e1 1530g1 850a1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 170c1

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	-1	+	-1	-6	-3	5	8	6	-10	-3	-3	3	11	2	9	11	8	-12	15	-7

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Quadratic twists for elliptic curve 170c1

-4	8	-3	5	-7	-11	13	17	-19	-23
1360d1	5440e1	1530g1	850a1	8330y1	20570b1	28730k1	2890q1	61370d1	89930bg1

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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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