Cremona's table of elliptic curves

4056 = 2³ · 3 · 13²

Field	Data	Notes
Atkin-Lehner	2- 3- 13-	Signs for the Atkin-Lehner involutions
Class	4056r	Isogeny class
Conductor	4056	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	576	Modular degree for the optimal curve
Δ	-1687296 = -1 · 28 · 3 · 133	Discriminant
Eigenvalues	2- 3- -2  2  4 13- -6  2	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-4,-64]	[a1,a2,a3,a4,a6]
j	-16/3	j-invariant
L	2.369471590263	L(r)(E,1)/r!
Ω	1.1847357951315	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	8112g1 32448o1 12168j1 101400p1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4056r1

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

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Quadratic twists for elliptic curve 4056r1

-4	8	-3	5	13
8112g1	32448o1	12168j1	101400p1	4056i1

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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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