Cremona's table of elliptic curves

17360 = 2⁴ · 5 · 7 · 31

Field	Data	Notes
Atkin-Lehner	2- 5+ 7- 31-	Signs for the Atkin-Lehner involutions
Class	17360ba	Isogeny class
Conductor	17360	Conductor
∏ cp	26	Product of Tamagawa factors cp
deg	14152320	Modular degree for the optimal curve
Δ	2.0640302499577E+26	Discriminant
Eigenvalues	2- -3 5+ 7-  5  1 -4  3	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-284726083,1715178217282]	[a1,a2,a3,a4,a6]
j	623225944950388227633972249/50391363524359094272000	j-invariant
L	1.4307204634426	L(r)(E,1)/r!
Ω	0.055027710132406	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	2170b1 69440ee1 86800bk1 121520cr1	Quadratic twists by: -4 8 5 -7

Hecke Eigenvalues for elliptic curve 17360ba1

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	+	-	5	1	-4	3	9	-10	-	4	2	12	-5	10	3	12	4	-7	8	4	7	-3	17

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Quadratic twists for elliptic curve 17360ba1

-4	8	5	-7
2170b1	69440ee1	86800bk1	121520cr1

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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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