Cremona's table of elliptic curves

4209 = 3 · 23 · 61

Field	Data	Notes
Atkin-Lehner	3- 23+ 61-	Signs for the Atkin-Lehner involutions
Class	4209b	Isogeny class
Conductor	4209	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	336	Modular degree for the optimal curve
Δ	-12627 = -1 · 32 · 23 · 61	Discriminant
Eigenvalues	2 3-  0 -3 -1 -1  6 -6	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,2,-5]	[a1,a2,a3,a4,a6]
Generators	[10:5:8]	Generators of the group modulo torsion
j	512000/12627	j-invariant
L	7.4047038145889	L(r)(E,1)/r!
Ω	1.9356523020351	Real period
R	1.9127153690784	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	67344n1 12627c1 105225g1 96807e1	Quadratic twists by: -4 -3 5 -23

Hecke Eigenvalues for elliptic curve 4209b1

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	-	0	-3	-1	-1	6	-6	+	-2	-8	-6	3	-1	-3	9	2	-	-11	10	-1	-1	6	14	-4

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Quadratic twists for elliptic curve 4209b1

-4	-3	5	-23
67344n1	12627c1	105225g1	96807e1

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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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