Cremona's table of elliptic curves

658 = 2 · 7 · 47

Field	Data	Notes
Atkin-Lehner	2+ 7+ 47-	Signs for the Atkin-Lehner involutions
Class	658b	Isogeny class
Conductor	658	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	865928 = 23 · 72 · 472	Discriminant
Eigenvalues	2+  2  2 7+ -2  2  6  4	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-49,-147]	[a1,a2,a3,a4,a6]
j	13430356633/865928	j-invariant
L	1.806990031054	L(r)(E,1)/r!
Ω	1.806990031054	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	5264k2 21056h2 5922o2 16450n2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 658b2

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	2	6	4	8	-4	8	-10	6	2	-	-14	-6	0	-14	16	-2	-16	14	-6	-2

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Quadratic twists for elliptic curve 658b2

-4	8	-3	5	-7	-11	13	-47
5264k2	21056h2	5922o2	16450n2	4606c2	79618bf2	111202x2	30926d2

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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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