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	4018b	Isogeny class
Conductor	4018	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	2304	Modular degree for the optimal curve
Δ	-6300224 = -1 · 26 · 74 · 41	Discriminant
Eigenvalues	2+ -3 -1 7+ -5  6  0  1	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-205,1189]	[a1,a2,a3,a4,a6]
Generators	[2:27:1]	Generators of the group modulo torsion
j	-397909449/2624	j-invariant
L	1.3765493302129	L(r)(E,1)/r!
Ω	2.3949855679064	Real period
R	0.095793850052037	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	32144l1 128576g1 36162ca1 100450bg1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4018b1

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 4018b1

-4	8	-3	5	-7
32144l1	128576g1	36162ca1	100450bg1	4018j1

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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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