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	4147a	Isogeny class
Conductor	4147	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	2496	Modular degree for the optimal curve
Δ	-1314835379 = -1 · 11 · 132 · 294	Discriminant
Eigenvalues	0  3  3  2 11+ 13-  0  6	Hecke eigenvalues for primes up to 20
Equation	[0,0,1,134,1639]	[a1,a2,a3,a4,a6]
j	266095853568/1314835379	j-invariant
L	4.3887209654622	L(r)(E,1)/r!
Ω	1.0971802413655	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	66352o1 37323m1 103675c1 45617c1	Quadratic twists by: -4 -3 5 -11

Hecke Eigenvalues for elliptic curve 4147a1

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
0	3	3	2	+	-	0	6	-1	+	-3	5	2	-8	-4	2	-5	2	-5	-5	4	0	0	17	-13

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Quadratic twists for elliptic curve 4147a1

-4	-3	5	-11	13	29
66352o1	37323m1	103675c1	45617c1	53911c1	120263g1

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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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