Cremona's table of elliptic curves

17640 = 2³ · 3² · 5 · 7²

Field	Data	Notes
Atkin-Lehner	2- 3- 5- 7-	Signs for the Atkin-Lehner involutions
Class	17640cs	Isogeny class
Conductor	17640	Conductor
∏ cp	32	Product of Tamagawa factors cp
Δ	-54890317440000 = -1 · 210 · 36 · 54 · 76	Discriminant
Eigenvalues	2- 3- 5- 7- -4  2  2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,5733,-314874]	[a1,a2,a3,a4,a6]
Generators	[91:980:1]	Generators of the group modulo torsion
j	237276/625	j-invariant
L	5.1918055919648	L(r)(E,1)/r!
Ω	0.32392535819022	Real period
R	2.0034729686537	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	35280ck3 1960b4 88200ct3 360e4	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 17640cs4

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
-	-	-	-	-4	2	2	-4	-4	2	8	6	-6	-8	4	-6	-4	2	8	0	6	0	-16	-6	14

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Quadratic twists for elliptic curve 17640cs4

-4	-3	5	-7
35280ck3	1960b4	88200ct3	360e4

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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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