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	17040h	Isogeny class
Conductor	17040	Conductor
∏ cp	64	Product of Tamagawa factors cp
Δ	211673606400000 = 211 · 38 · 55 · 712	Discriminant
Eigenvalues	2+ 3- 5+  2 -2 -2  4 -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-131416,-18367180]	[a1,a2,a3,a4,a6]
Generators	[-214:36:1]	Generators of the group modulo torsion
j	122558037185240498/103356253125	j-invariant
L	5.917174632393	L(r)(E,1)/r!
Ω	0.2507605450091	Real period
R	1.4748070295953	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	8520c2 68160ct2 51120i2 85200k2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 17040h2

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	-2	4	-4	2	-2	8	-2	-6	-4	-6	-6	10	4	-12	-	2	-16	-4	6	16

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Quadratic twists for elliptic curve 17040h2

-4	8	-3	5
8520c2	68160ct2	51120i2	85200k2

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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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