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	32	Product of Tamagawa factors cp
Δ	137768960000 = 215 · 54 · 7 · 312	Discriminant
Eigenvalues	2- -2 5- 7+  0  2  4 -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-4520,114100]	[a1,a2,a3,a4,a6]
Generators	[30:80:1]	Generators of the group modulo torsion
j	2493877677481/33635000	j-invariant
L	3.4422995287772	L(r)(E,1)/r!
Ω	1.0390620719229	Real period
R	0.41411139211428	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	2170g2 69440cg2 86800bw2 121520bz2	Quadratic twists by: -4 8 5 -7

Hecke Eigenvalues for elliptic curve 17360bf2

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 17360bf2

-4	8	5	-7
2170g2	69440cg2	86800bw2	121520bz2

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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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