Cremona's table of elliptic curves

4128 = 2⁵ · 3 · 43

Field	Data	Notes
Atkin-Lehner	2- 3- 43+	Signs for the Atkin-Lehner involutions
Class	4128m	Isogeny class
Conductor	4128	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	384	Modular degree for the optimal curve
Δ	-1585152 = -1 · 212 · 32 · 43	Discriminant
Eigenvalues	2- 3-  0  2 -3 -1 -1  0	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-13,59]	[a1,a2,a3,a4,a6]
Generators	[5:12:1]	Generators of the group modulo torsion
j	-64000/387	j-invariant
L	4.4154175057513	L(r)(E,1)/r!
Ω	2.306427804584	Real period
R	0.47859914550282	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	4128k1 8256bi1 12384d1 103200h1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4128m1

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
-	-	0	2	-3	-1	-1	0	-3	-8	-9	2	-9	+	0	5	-4	10	5	-6	6	0	13	-10	-9

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Quadratic twists for elliptic curve 4128m1

-4	8	-3	5
4128k1	8256bi1	12384d1	103200h1

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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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