Cremona's table of elliptic curves

4862 = 2 · 11 · 13 · 17

Field	Data	Notes
Atkin-Lehner	2+ 11+ 13- 17-	Signs for the Atkin-Lehner involutions
Class	4862c	Isogeny class
Conductor	4862	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	20847389708288 = 212 · 116 · 132 · 17	Discriminant
Eigenvalues	2+ -2  0 -4 11+ 13- 17- -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-627151,-191215998]	[a1,a2,a3,a4,a6]
Generators	[237261:22029196:27]	Generators of the group modulo torsion
j	27279667585959979515625/20847389708288	j-invariant
L	1.4828441881651	L(r)(E,1)/r!
Ω	0.16965107963306	Real period
R	4.3702763087991	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	38896m3 43758w3 121550be3 53482l3	Quadratic twists by: -4 -3 5 -11

Hecke Eigenvalues for elliptic curve 4862c3

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	-4	+	-	-	-4	6	-6	8	-4	0	8	0	-6	12	14	-4	-12	8	14	12	6	-16

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Quadratic twists for elliptic curve 4862c3

-4	-3	5	-11	13	17
38896m3	43758w3	121550be3	53482l3	63206o3	82654g3

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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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