Cremona's table of elliptic curves

17040 = 2⁴ · 3 · 5 · 71

Field	Data	Notes
Atkin-Lehner	2- 3+ 5+ 71-	Signs for the Atkin-Lehner involutions
Class	17040n	Isogeny class
Conductor	17040	Conductor
∏ cp	48	Product of Tamagawa factors cp
Δ	-118746279936000000 = -1 · 218 · 34 · 56 · 713	Discriminant
Eigenvalues	2- 3+ 5+ -2 -6  2  0  4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,71304,-14895504]	[a1,a2,a3,a4,a6]
Generators	[668:18176:1]	Generators of the group modulo torsion
j	9788121552577031/28990791000000	j-invariant
L	3.0047697263106	L(r)(E,1)/r!
Ω	0.16999733996169	Real period
R	1.4729493840844	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	2130d3 68160dq3 51120bm3 85200df3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 17040n3

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

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Quadratic twists for elliptic curve 17040n3

-4	8	-3	5
2130d3	68160dq3	51120bm3	85200df3

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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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