Cremona's table of elliptic curves

117249 = 3 · 11² · 17 · 19

Field	Data	Notes
Atkin-Lehner	3- 11- 17- 19-	Signs for the Atkin-Lehner involutions
Class	117249bd	Isogeny class
Conductor	117249	Conductor
∏ cp	117	Product of Tamagawa factors cp
deg	140107968	Modular degree for the optimal curve
Δ	-2.2684775879525E+29	Discriminant
Eigenvalues	-1 3-  3 -3 11- -2 17- 19-	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-4007739799,-100308544861678]	[a1,a2,a3,a4,a6]
Generators	[75529:5240236:1]	Generators of the group modulo torsion
j	-274470335171486440642777/8745963112563846489	j-invariant
L	5.6346653067796	L(r)(E,1)/r!
Ω	0.0094695777262415	Real period
R	5.0857106678274	Regulator
r	1	Rank of the group of rational points
S	1.0000000015451	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	117249l1	Quadratic twists by: -11

Hecke Eigenvalues for elliptic curve 117249bd1

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
-1	-	3	-3	-	-2	-	-	0	0	-4	-7	-2	6	9	-11	6	2	3	13	4	6	4	-14	-13

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Quadratic twists for elliptic curve 117249bd1

-11
117249l1

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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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