Cremona's table of elliptic curves

15884 = 2² · 11 · 19²

Field	Data	Notes
Atkin-Lehner	2- 11- 19-	Signs for the Atkin-Lehner involutions
Class	15884m	Isogeny class
Conductor	15884	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	4752	Modular degree for the optimal curve
Δ	698896 = 24 · 112 · 192	Discriminant
Eigenvalues	2- -3 -1 -4 11- -1 -3 19-	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-133,589]	[a1,a2,a3,a4,a6]
Generators	[-13:11:1] [4:11:1]	Generators of the group modulo torsion
j	45045504/121	j-invariant
L	3.8961389651312	L(r)(E,1)/r!
Ω	2.8701032033521	Real period
R	0.22624848243439	Regulator
r	2	Rank of the group of rational points
S	1.0000000000001	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	63536z1 15884j1	Quadratic twists by: -4 -19

Hecke Eigenvalues for elliptic curve 15884m1

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	-1	-4	-	-1	-3	-	1	-9	0	-2	3	1	-11	-3	9	1	-1	9	-11	3	-12	-11	17

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Quadratic twists for elliptic curve 15884m1

-4	-19
63536z1	15884j1

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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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