Cremona's table of elliptic curves

4418 = 2 · 47²

Field	Data	Notes
Atkin-Lehner	2- 47-	Signs for the Atkin-Lehner involutions
Class	4418b	Isogeny class
Conductor	4418	Conductor
∏ cp	30	Product of Tamagawa factors cp
deg	45120	Modular degree for the optimal curve
Δ	-24382757541643264 = -1 · 210 · 478	Discriminant
Eigenvalues	2-  0  3  0 -4 -1 -5 -8	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-240091,-45839477]	[a1,a2,a3,a4,a6]
Generators	[1657:63232:1]	Generators of the group modulo torsion
j	-64278657/1024	j-invariant
L	5.8607123430576	L(r)(E,1)/r!
Ω	0.10773696538327	Real period
R	1.8132780834039	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	35344b1 39762n1 110450c1 4418c1	Quadratic twists by: -4 -3 5 -47

Hecke Eigenvalues for elliptic curve 4418b1

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
-	0	3	0	-4	-1	-5	-8	4	-2	4	-10	-6	0	-	11	-12	-1	8	-4	10	8	-4	-13	-5

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Quadratic twists for elliptic curve 4418b1

-4	-3	5	-47
35344b1	39762n1	110450c1	4418c1

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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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