Cremona's table of elliptic curves

4018 = 2 · 7² · 41

Field	Data	Notes
Atkin-Lehner	2- 7- 41-	Signs for the Atkin-Lehner involutions
Class	4018s	Isogeny class
Conductor	4018	Conductor
∏ cp	42	Product of Tamagawa factors cp
deg	169344	Modular degree for the optimal curve
Δ	8330830260075495424 = 221 · 713 · 41	Discriminant
Eigenvalues	2-  3  1 7- -2  0  3  8	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-948282,-326942087]	[a1,a2,a3,a4,a6]
j	801581275315909089/70810888830976	j-invariant
L	6.4618543473744	L(r)(E,1)/r!
Ω	0.15385367493749	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	32144bf1 128576bu1 36162r1 100450u1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4018s1

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
-	3	1	-	-2	0	3	8	-4	-5	3	10	-	-5	-6	-9	10	-13	-2	9	-4	-11	14	1	-7

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Quadratic twists for elliptic curve 4018s1

-4	8	-3	5	-7
32144bf1	128576bu1	36162r1	100450u1	574i1

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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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