Cremona's table of elliptic curves

147 = 3 · 7²

Field	Data	Notes
Atkin-Lehner	3+ 7-	Signs for the Atkin-Lehner involutions
Class	147a	Isogeny class
Conductor	147	Conductor
∏ cp	2	Product of Tamagawa factors cp
Δ	17294403 = 3 · 78	Discriminant
Eigenvalues	-1 3+  2 7-  4  2  6 -4	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-38417,2882228]	[a1,a2,a3,a4,a6]
j	53297461115137/147	j-invariant
L	0.72228624540788	L(r)(E,1)/r!
Ω	1.4445724908158	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	2352v5 9408bj5 441c5 3675j5	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 147a5

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	-	4	2	6	-4	0	-2	0	6	-2	-4	0	6	-12	2	4	0	6	-16	12	14	-18

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Quadratic twists for elliptic curve 147a5

-4	8	-3	5	-7	-11	13	17	-19	-23	29
2352v5	9408bj5	441c5	3675j5	21a5	17787h5	24843d6	42483v6	53067q6	77763l6	123627r6

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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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