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	17360s	Isogeny class
Conductor	17360	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	675067904000 = 214 · 53 · 73 · 312	Discriminant
Eigenvalues	2-  2 5+ 7+ -6  2 -6  4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-14634656,21553619456]	[a1,a2,a3,a4,a6]
j	84627468364197487202209/164811500	j-invariant
L	1.6644772835068	L(r)(E,1)/r!
Ω	0.41611932087671	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	4	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	2170n4 69440dg4 86800bz4 121520dc4	Quadratic twists by: -4 8 5 -7

Hecke Eigenvalues for elliptic curve 17360s4

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	+	+	-6	2	-6	4	0	6	+	-4	-6	-8	0	0	-12	8	4	-12	14	10	6	12	2

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Quadratic twists for elliptic curve 17360s4

-4	8	5	-7
2170n4	69440dg4	86800bz4	121520dc4

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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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