Cremona's table of elliptic curves

39072 = 2⁵ · 3 · 11 · 37

Field	Data	Notes
Atkin-Lehner	2- 3- 11- 37-	Signs for the Atkin-Lehner involutions
Class	39072r	Isogeny class
Conductor	39072	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	12544	Modular degree for the optimal curve
Δ	-16879104 = -1 · 29 · 34 · 11 · 37	Discriminant
Eigenvalues	2- 3-  3 -4 11-  0 -3  4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-144,648]	[a1,a2,a3,a4,a6]
Generators	[6:-6:1]	Generators of the group modulo torsion
j	-649461896/32967	j-invariant
L	7.7051872956334	L(r)(E,1)/r!
Ω	2.1693324958895	Real period
R	0.44398376633345	Regulator
r	1	Rank of the group of rational points
S	0.99999999999961	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	39072l1 78144bu1 117216k1	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 39072r1

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
-	-	3	-4	-	0	-3	4	-6	-8	-2	-	6	10	7	-12	12	6	-12	9	-4	-11	3	-4	2

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Quadratic twists for elliptic curve 39072r1

-4	8	-3
39072l1	78144bu1	117216k1

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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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