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	8	Product of Tamagawa factors cp
deg	24	Modular degree for the optimal curve
Δ	-7411887 = -1 · 32 · 77	Discriminant
Eigenvalues	-1 3+  2 7-  4  2  6 -4	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,48,48]	[a1,a2,a3,a4,a6]
j	103823/63	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	4	Number of elements in the torsion subgroup
Twists	2352v1 9408bj1 441c1 3675j1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 147a1

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 147a1

-4	8	-3	5	-7	-11	13	17	-19	-23	29
2352v1	9408bj1	441c1	3675j1	21a4	17787h1	24843d1	42483v1	53067q1	77763l1	123627r1

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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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