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	-754628826325811008 = -1 · 26 · 1112 · 13 · 172	Discriminant
Eigenvalues	2+ -2  0 -4 11+ 13- 17- -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-622991,-193876734]	[a1,a2,a3,a4,a6]
Generators	[73780:1557083:64]	Generators of the group modulo torsion
j	-26740407923656692603625/754628826325811008	j-invariant
L	1.4828441881651	L(r)(E,1)/r!
Ω	0.084825539816531	Real period
R	8.7405526175982	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	38896m4 43758w4 121550be4 53482l4	Quadratic twists by: -4 -3 5 -11

Hecke Eigenvalues for elliptic curve 4862c4

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 4862c4

-4	-3	5	-11	13	17
38896m4	43758w4	121550be4	53482l4	63206o4	82654g4

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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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