Cremona's table of elliptic curves

17472 = 2⁶ · 3 · 7 · 13

Field	Data	Notes
Atkin-Lehner	2- 3- 7+ 13-	Signs for the Atkin-Lehner involutions
Class	17472cu	Isogeny class
Conductor	17472	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	49093804032 = 219 · 3 · 74 · 13	Discriminant
Eigenvalues	2- 3- -2 7+ -4 13-  6 -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-26689,-1687105]	[a1,a2,a3,a4,a6]
j	8020417344913/187278	j-invariant
L	1.4940864359222	L(r)(E,1)/r!
Ω	0.37352160898055	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	17472o3 4368o3 52416fj4 122304fi4	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 17472cu3

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

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Quadratic twists for elliptic curve 17472cu3

-4	8	-3	-7
17472o3	4368o3	52416fj4	122304fi4

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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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