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	17360q	Isogeny class
Conductor	17360	Conductor
∏ cp	2	Product of Tamagawa factors cp
Δ	41854210048000 = 215 · 53 · 73 · 313	Discriminant
Eigenvalues	2- -1 5+ 7+ -3  5 -6  7	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-10456,-265744]	[a1,a2,a3,a4,a6]
j	30867540216409/10218313000	j-invariant
L	0.96930197330201	L(r)(E,1)/r!
Ω	0.48465098665101	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	2170c2 69440dd2 86800bt2 121520cy2	Quadratic twists by: -4 8 5 -7

Hecke Eigenvalues for elliptic curve 17360q2

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
-	-1	+	+	-3	5	-6	7	9	-6	+	2	0	-8	3	0	-9	8	4	15	-16	10	-15	-15	-1

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Quadratic twists for elliptic curve 17360q2

-4	8	5	-7
2170c2	69440dd2	86800bt2	121520cy2

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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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