Cremona's table of elliptic curves

4147 = 11 · 13 · 29

Field	Data	Notes
Atkin-Lehner	11+ 13- 29-	Signs for the Atkin-Lehner involutions
Class	4147b	Isogeny class
Conductor	4147	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	4416	Modular degree for the optimal curve
Δ	-31970355131 = -1 · 113 · 134 · 292	Discriminant
Eigenvalues	-2  1 -3  0 11+ 13-  4  6	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,58,8620]	[a1,a2,a3,a4,a6]
Generators	[29:188:1]	Generators of the group modulo torsion
j	21207928832/31970355131	j-invariant
L	1.7107115554429	L(r)(E,1)/r!
Ω	0.91621463461737	Real period
R	0.23339394106018	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	66352r1 37323l1 103675g1 45617b1	Quadratic twists by: -4 -3 5 -11

Hecke Eigenvalues for elliptic curve 4147b1

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	1	-3	0	+	-	4	6	-5	-	-7	5	0	12	-8	-6	9	10	13	-3	-2	-14	14	1	15

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Quadratic twists for elliptic curve 4147b1

-4	-3	5	-11	13	29
66352r1	37323l1	103675g1	45617b1	53911d1	120263h1

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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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