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	2	Product of Tamagawa factors cp
Δ	-46512704 = -1 · 26 · 7 · 473	Discriminant
Eigenvalues	2+  1  3 7-  3  2  0  2	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-32,-338]	[a1,a2,a3,a4,a6]
j	-3463512697/46512704	j-invariant
L	1.7237634876104	L(r)(E,1)/r!
Ω	0.86188174380522	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	5264f2 21056k2 5922r2 16450j2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 658c2

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 658c2

-4	8	-3	5	-7	-11	13	-47
5264f2	21056k2	5922r2	16450j2	4606f2	79618t2	111202r2	30926e2

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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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