Cremona's table of elliptic curves

17340 = 2² · 3 · 5 · 17²

Field	Data	Notes
Atkin-Lehner	2- 3- 5+ 17+	Signs for the Atkin-Lehner involutions
Class	17340n	Isogeny class
Conductor	17340	Conductor
∏ cp	28	Product of Tamagawa factors cp
deg	48384	Modular degree for the optimal curve
Δ	-71792854228080 = -1 · 24 · 37 · 5 · 177	Discriminant
Eigenvalues	2- 3- 5+ -3 -1 -2 17+  1	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,8574,272709]	[a1,a2,a3,a4,a6]
Generators	[45:867:1]	Generators of the group modulo torsion
j	180472064/185895	j-invariant
L	4.7190901997106	L(r)(E,1)/r!
Ω	0.40628599085448	Real period
R	0.41482832166939	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	69360ce1 52020bg1 86700g1 1020d1	Quadratic twists by: -4 -3 5 17

Hecke Eigenvalues for elliptic curve 17340n1

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
-	-	+	-3	-1	-2	+	1	-6	-7	10	3	9	8	3	5	8	-10	16	-12	9	-2	12	0	2

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Quadratic twists for elliptic curve 17340n1

-4	-3	5	17
69360ce1	52020bg1	86700g1	1020d1

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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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