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	17360bf	Isogeny class
Conductor	17360	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	9216	Modular degree for the optimal curve
Δ	-9954918400 = -1 · 218 · 52 · 72 · 31	Discriminant
Eigenvalues	2- -2 5- 7+  0  2  4 -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-40,4788]	[a1,a2,a3,a4,a6]
Generators	[-4:70:1]	Generators of the group modulo torsion
j	-1771561/2430400	j-invariant
L	3.4422995287772	L(r)(E,1)/r!
Ω	1.0390620719229	Real period
R	0.82822278422857	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	2170g1 69440cg1 86800bw1 121520bz1	Quadratic twists by: -4 8 5 -7

Hecke Eigenvalues for elliptic curve 17360bf1

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

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Quadratic twists for elliptic curve 17360bf1

-4	8	5	-7
2170g1	69440cg1	86800bw1	121520bz1

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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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