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	4056j	Isogeny class
Conductor	4056	Conductor
∏ cp	32	Product of Tamagawa factors cp
deg	2304	Modular degree for the optimal curve
Δ	230632272 = 24 · 38 · 133	Discriminant
Eigenvalues	2+ 3- -4 -2  2 13-  6 -2	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-355,2354]	[a1,a2,a3,a4,a6]
Generators	[5:27:1]	Generators of the group modulo torsion
j	141150208/6561	j-invariant
L	3.279228556273	L(r)(E,1)/r!
Ω	1.7447363302002	Real period
R	0.23493725810541	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	8112i1 32448u1 12168x1 101400ci1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4056j1

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

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Quadratic twists for elliptic curve 4056j1

-4	8	-3	5	13
8112i1	32448u1	12168x1	101400ci1	4056s1

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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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