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	170b	Isogeny class
Conductor	170	Conductor
∏ cp	12	Product of Tamagawa factors cp
deg	160	Modular degree for the optimal curve
Δ	31443200 = 28 · 52 · 173	Discriminant
Eigenvalues	2+ -2 5+  2  6  2 17-  8	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-2554,49452]	[a1,a2,a3,a4,a6]
j	1841373668746009/31443200	j-invariant
L	0.63726065819045	L(r)(E,1)/r!
Ω	1.9117819745714	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	6	Number of elements in the torsion subgroup
Twists	1360f1 5440l1 1530p1 850h1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 170b1

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	6	2	-	8	-6	-6	2	2	-6	-4	12	6	0	2	8	-6	2	-10	12	6	2

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Quadratic twists for elliptic curve 170b1

-4	8	-3	5	-7	-11	13	17	-19	-23
1360f1	5440l1	1530p1	850h1	8330k1	20570j1	28730bc1	2890i1	61370s1	89930q1

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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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