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	72	Product of Tamagawa factors cp
deg	19584	Modular degree for the optimal curve
Δ	45910522026512 = 24 · 112 · 136 · 173	Discriminant
Eigenvalues	2+ -2  0 -4 11+ 13- 17- -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-9456,-138514]	[a1,a2,a3,a4,a6]
Generators	[-16:101:1]	Generators of the group modulo torsion
j	93493211839989625/45910522026512	j-invariant
L	1.4828441881651	L(r)(E,1)/r!
Ω	0.50895323889919	Real period
R	1.4567587695997	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	6	Number of elements in the torsion subgroup
Twists	38896m1 43758w1 121550be1 53482l1	Quadratic twists by: -4 -3 5 -11

Hecke Eigenvalues for elliptic curve 4862c1

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 4862c1

-4	-3	5	-11	13	17
38896m1	43758w1	121550be1	53482l1	63206o1	82654g1

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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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