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	17040i	Isogeny class
Conductor	17040	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	1951617100800 = 210 · 3 · 52 · 714	Discriminant
Eigenvalues	2+ 3- 5- -4 -4 -2  6 -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-3280,-27772]	[a1,a2,a3,a4,a6]
Generators	[91:660:1]	Generators of the group modulo torsion
j	3812217641284/1905876075	j-invariant
L	5.2866925726905	L(r)(E,1)/r!
Ω	0.66447985857841	Real period
R	3.9780683375422	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	8520j3 68160bz4 51120c4 85200d4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 17040i3

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
+	-	-	-4	-4	-2	6	-4	0	6	4	6	6	-4	0	-6	4	-2	0	+	-6	0	-12	-14	18

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Quadratic twists for elliptic curve 17040i3

-4	8	-3	5
8520j3	68160bz4	51120c4	85200d4

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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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