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	658c	Isogeny class
Conductor	658	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	48	Modular degree for the optimal curve
Δ	-64484 = -1 · 22 · 73 · 47	Discriminant
Eigenvalues	2+  1  3 7-  3  2  0  2	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,3,12]	[a1,a2,a3,a4,a6]
j	4657463/64484	j-invariant
L	1.7237634876104	L(r)(E,1)/r!
Ω	2.5856452314157	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	3	Number of elements in the torsion subgroup
Twists	5264f1 21056k1 5922r1 16450j1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 658c1

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	3	-	3	2	0	2	0	0	-4	-1	-3	-1	+	9	9	-4	8	-6	-7	2	9	0	-16

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Quadratic twists for elliptic curve 658c1

-4	8	-3	5	-7	-11	13	-47
5264f1	21056k1	5922r1	16450j1	4606f1	79618t1	111202r1	30926e1

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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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