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	4018j	Isogeny class
Conductor	4018	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	16128	Modular degree for the optimal curve
Δ	-741215053376 = -1 · 26 · 710 · 41	Discriminant
Eigenvalues	2+  3  1 7- -5 -6  0 -1	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-10054,-387724]	[a1,a2,a3,a4,a6]
Generators	[208260:3155554:729]	Generators of the group modulo torsion
j	-397909449/2624	j-invariant
L	4.3815348858923	L(r)(E,1)/r!
Ω	0.23829322252381	Real period
R	9.1935784817684	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	32144bg1 128576bv1 36162cl1 100450cd1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4018j1

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	-	-5	-6	0	-1	-4	-8	-6	-2	-	4	0	6	-2	-13	16	-3	2	-11	14	-14	8

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Quadratic twists for elliptic curve 4018j1

-4	8	-3	5	-7
32144bg1	128576bv1	36162cl1	100450cd1	4018b1

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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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