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	40128ba	Isogeny class
Conductor	40128	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	147456	Modular degree for the optimal curve
Δ	8386752 = 26 · 3 · 112 · 192	Discriminant
Eigenvalues	2+ 3- -2 -4 11-  2 -6 19+	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-174724,28052882]	[a1,a2,a3,a4,a6]
Generators	[6699:5192:27]	Generators of the group modulo torsion
j	9217304063844205888/131043	j-invariant
L	4.8518415128393	L(r)(E,1)/r!
Ω	1.184973616941	Real period
R	4.0944721835791	Regulator
r	1	Rank of the group of rational points
S	0.99999999999983	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	40128h1 20064q3 120384r1	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 40128ba1

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	-4	-	2	-6	+	8	6	4	-6	-6	-12	0	6	12	-14	-12	8	-6	12	4	18	-14

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Quadratic twists for elliptic curve 40128ba1

-4	8	-3
40128h1	20064q3	120384r1

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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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