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	4147c	Isogeny class
Conductor	4147	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	2880	Modular degree for the optimal curve
Δ	-589408963 = -1 · 11 · 133 · 293	Discriminant
Eigenvalues	1  2 -2 -5 11- 13+  1  0	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-676,6591]	[a1,a2,a3,a4,a6]
j	-34242639807817/589408963	j-invariant
L	1.6345871501337	L(r)(E,1)/r!
Ω	1.6345871501337	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	66352g1 37323d1 103675x1 45617d1	Quadratic twists by: -4 -3 5 -11

Hecke Eigenvalues for elliptic curve 4147c1

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	2	-2	-5	-	+	1	0	5	+	7	3	10	-12	11	-3	2	-3	14	-6	10	5	-12	-15	2

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Quadratic twists for elliptic curve 4147c1

-4	-3	5	-11	13	29
66352g1	37323d1	103675x1	45617d1	53911a1	120263b1

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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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