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	2	Product of Tamagawa factors cp
deg	72	Modular degree for the optimal curve
Δ	21056 = 26 · 7 · 47	Discriminant
Eigenvalues	2+  2  2 7+ -2  2  6  4	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-9,5]	[a1,a2,a3,a4,a6]
j	95443993/21056	j-invariant
L	1.806990031054	L(r)(E,1)/r!
Ω	3.613980062108	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	5264k1 21056h1 5922o1 16450n1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 658b1

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 658b1

-4	8	-3	5	-7	-11	13	-47
5264k1	21056h1	5922o1	16450n1	4606c1	79618bf1	111202x1	30926d1

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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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