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	17472cn	Isogeny class
Conductor	17472	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	-2906279620608 = -1 · 212 · 3 · 72 · 136	Discriminant
Eigenvalues	2- 3- -2 7+  0 13+ -4 -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-20489,-1138665]	[a1,a2,a3,a4,a6]
Generators	[24552357:771046332:24389]	Generators of the group modulo torsion
j	-232245467895232/709540923	j-invariant
L	4.8124162691569	L(r)(E,1)/r!
Ω	0.19948403578424	Real period
R	12.062158884638	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	17472ce2 8736o1 52416eq2 122304gb2	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 17472cn2

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	+	-4	-4	6	6	0	6	-6	4	2	6	-6	14	-4	4	6	-4	-6	-2	-6

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Quadratic twists for elliptic curve 17472cn2

-4	8	-3	-7
17472ce2	8736o1	52416eq2	122304gb2

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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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