Cremona's table of elliptic curves

4686 = 2 · 3 · 11 · 71

Field	Data	Notes
Atkin-Lehner	2+ 3+ 11- 71-	Signs for the Atkin-Lehner involutions
Class	4686a	Isogeny class
Conductor	4686	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	174283431499584 = 26 · 320 · 11 · 71	Discriminant
Eigenvalues	2+ 3+ -2  0 11- -2  2  0	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-267811,-53452595]	[a1,a2,a3,a4,a6]
Generators	[-1014735:652831:3375]	Generators of the group modulo torsion
j	2124278626065664981177/174283431499584	j-invariant
L	1.9984679529689	L(r)(E,1)/r!
Ω	0.20986710838597	Real period
R	9.5225400890044	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	37488y4 14058f4 117150cb4 51546g4	Quadratic twists by: -4 -3 5 -11

Hecke Eigenvalues for elliptic curve 4686a3

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	-	-2	2	0	0	2	-4	6	2	-8	8	2	4	-2	8	-	2	4	12	-14	-6

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Quadratic twists for elliptic curve 4686a3

-4	-3	5	-11
37488y4	14058f4	117150cb4	51546g4

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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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