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	13	Product of Tamagawa factors cp
Δ	-9190954824723 = -1 · 313 · 78	Discriminant
Eigenvalues	2 3- -2 7+ -2  1  0  1	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,-44704,-3655907]	[a1,a2,a3,a4,a6]
j	-1713910976512/1594323	j-invariant
L	2.1340337344824	L(r)(E,1)/r!
Ω	0.16415644111403	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	2352j2 9408c2 441e2 3675d2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 147b2

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 147b2

-4	8	-3	5	-7	-11	13	17	-19	-23	29
2352j2	9408c2	441e2	3675d2	147c2	17787m2	24843o2	42483c2	53067d2	77763ba2	123627a2

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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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