Cremona's table of elliptic curves

147 = 3 · 7²

Field	Data	Notes
Atkin-Lehner	3- 7+	Signs for the Atkin-Lehner involutions
Class	147b	Isogeny class
Conductor	147	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	42	Modular degree for the optimal curve
Δ	-17294403 = -1 · 3 · 78	Discriminant
Eigenvalues	2 3- -2 7+ -2  1  0  1	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,-114,473]	[a1,a2,a3,a4,a6]
j	-28672/3	j-invariant
L	2.1340337344824	L(r)(E,1)/r!
Ω	2.1340337344824	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	2352j1 9408c1 441e1 3675d1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 147b1

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	-	-2	+	-2	1	0	1	0	4	9	3	-10	5	-6	12	-12	10	-5	-6	-3	-1	6	16	-6

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Quadratic twists for elliptic curve 147b1

-4	8	-3	5	-7	-11	13	17	-19	-23	29
2352j1	9408c1	441e1	3675d1	147c1	17787m1	24843o1	42483c1	53067d1	77763ba1	123627a1

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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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