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	17040u	Isogeny class
Conductor	17040	Conductor
∏ cp	24	Product of Tamagawa factors cp
Δ	696867840000 = 213 · 33 · 54 · 712	Discriminant
Eigenvalues	2- 3- 5+ -2  2 -4 -4  4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-4016,88020]	[a1,a2,a3,a4,a6]
Generators	[-44:426:1]	Generators of the group modulo torsion
j	1749254553649/170133750	j-invariant
L	5.0712250483426	L(r)(E,1)/r!
Ω	0.87983769002234	Real period
R	0.96063647228195	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	2130h2 68160cm2 51120bs2 85200bp2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 17040u2

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	-4	-4	4	-4	-2	6	-2	8	4	8	6	2	-8	8	+	2	0	-8	-10	-6

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Quadratic twists for elliptic curve 17040u2

-4	8	-3	5
2130h2	68160cm2	51120bs2	85200bp2

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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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