Cremona's table of elliptic curves

40128 = 2⁶ · 3 · 11 · 19

Field	Data	Notes
Atkin-Lehner	2- 3+ 11+ 19+	Signs for the Atkin-Lehner involutions
Class	40128bf	Isogeny class
Conductor	40128	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	246114975744 = 215 · 33 · 114 · 19	Discriminant
Eigenvalues	2- 3+ -2  0 11+ -6 -2 19+	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-22049,1267329]	[a1,a2,a3,a4,a6]
Generators	[-155:968:1] [69:264:1]	Generators of the group modulo torsion
j	36179300529224/7510833	j-invariant
L	6.7678122265566	L(r)(E,1)/r!
Ω	0.95949829628972	Real period
R	3.5267453067548	Regulator
r	2	Rank of the group of rational points
S	0.99999999999979	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	40128ce4 20064l3 120384dh4	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 40128bf4

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
-	+	-2	0	+	-6	-2	+	0	-2	-4	10	6	-4	0	-6	-12	-2	-12	8	-6	8	12	6	-14

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Quadratic twists for elliptic curve 40128bf4

-4	8	-3
40128ce4	20064l3	120384dh4

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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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