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	4018o	Isogeny class
Conductor	4018	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	576	Modular degree for the optimal curve
Δ	112504 = 23 · 73 · 41	Discriminant
Eigenvalues	2- -1 -3 7-  4  2 -7  4	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-22,27]	[a1,a2,a3,a4,a6]
Generators	[-1:7:1]	Generators of the group modulo torsion
j	3442951/328	j-invariant
L	3.798667387444	L(r)(E,1)/r!
Ω	3.2408067493643	Real period
R	0.19535605798305	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	32144p1 128576o1 36162bi1 100450h1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4018o1

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
-	-1	-3	-	4	2	-7	4	-4	9	1	8	+	-3	-8	-11	-6	-9	-2	-7	-4	-15	4	-1	-5

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Quadratic twists for elliptic curve 4018o1

-4	8	-3	5	-7
32144p1	128576o1	36162bi1	100450h1	4018r1

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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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