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	7	Product of Tamagawa factors cp
Δ	-1228250000000 = -1 · 27 · 59 · 173	Discriminant
Eigenvalues	2-  1 5+  2  0 -1 17+ -1	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-6641,-215575]	[a1,a2,a3,a4,a6]
j	-32391289681150609/1228250000000	j-invariant
L	1.8469013549656	L(r)(E,1)/r!
Ω	0.26384305070938	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	1360d2 5440e2 1530g2 850a2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 170c2

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 170c2

-4	8	-3	5	-7	-11	13	17	-19	-23
1360d2	5440e2	1530g2	850a2	8330y2	20570b2	28730k2	2890q2	61370d2	89930bg2

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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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