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	17340b	Isogeny class
Conductor	17340	Conductor
∏ cp	12	Product of Tamagawa factors cp
deg	311040	Modular degree for the optimal curve
Δ	-403834805032950000 = -1 · 24 · 39 · 55 · 177	Discriminant
Eigenvalues	2- 3+ 5+  5  5  0 17+  1	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-49226,30878601]	[a1,a2,a3,a4,a6]
j	-34158804736/1045659375	j-invariant
L	3.0010061879561	L(r)(E,1)/r!
Ω	0.25008384899634	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	69360df1 52020bi1 86700bp1 1020h1	Quadratic twists by: -4 -3 5 17

Hecke Eigenvalues for elliptic curve 17340b1

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
-	+	+	5	5	0	+	1	8	3	8	3	-5	-4	1	-1	6	4	2	-8	17	-10	8	-18	14

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Quadratic twists for elliptic curve 17340b1

-4	-3	5	17
69360df1	52020bi1	86700bp1	1020h1

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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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