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	17040l	Isogeny class
Conductor	17040	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	-6175089229824000000 = -1 · 236 · 34 · 56 · 71	Discriminant
Eigenvalues	2- 3+ 5+ -2  0 -4  0  4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-24575976,46902020976]	[a1,a2,a3,a4,a6]
j	-400770830496236396186089/1507590144000000	j-invariant
L	0.83737036384355	L(r)(E,1)/r!
Ω	0.20934259096089	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	2130f3 68160df3 51120br3 85200cv3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 17040l3

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	0	-4	0	4	6	-6	4	2	-6	-8	6	0	0	2	-2	+	2	-8	12	-6	8

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Quadratic twists for elliptic curve 17040l3

-4	8	-3	5
2130f3	68160df3	51120br3	85200cv3

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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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