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	256	Product of Tamagawa factors cp
Δ	37609665859584 = 212 · 38 · 72 · 134	Discriminant
Eigenvalues	2- 3- -2 7-  0 13- -6 -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-36569,2663271]	[a1,a2,a3,a4,a6]
Generators	[-65:2184:1]	Generators of the group modulo torsion
j	1320428512222912/9182047329	j-invariant
L	5.2741142869728	L(r)(E,1)/r!
Ω	0.65254499721231	Real period
R	0.50514852514999	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	17472bw2 8736s1 52416gm2 122304ff2	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 17472dd2

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 17472dd2

-4	8	-3	-7
17472bw2	8736s1	52416gm2	122304ff2

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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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