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	17472dd	Isogeny class
Conductor	17472	Conductor
∏ cp	128	Product of Tamagawa factors cp
Δ	1076995325952 = 215 · 34 · 74 · 132	Discriminant
Eigenvalues	2- 3- -2 7-  0 13- -6 -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-584129,171640287]	[a1,a2,a3,a4,a6]
Generators	[91:10920:1]	Generators of the group modulo torsion
j	672668087746709384/32867289	j-invariant
L	5.2741142869728	L(r)(E,1)/r!
Ω	0.65254499721231	Real period
R	1.0102970503	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	17472bw3 8736s3 52416gm4 122304ff4	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 17472dd3

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

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Quadratic twists for elliptic curve 17472dd3

-4	8	-3	-7
17472bw3	8736s3	52416gm4	122304ff4

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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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